%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP132-1.002 : 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 : n019.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 06:38:57 EDT 2024 % Result : Unsatisfiable 76.13s 76.71s % Output : CNFRefutation 76.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GRP132-1.002 : TPTP v8.2.0. Released v1.2.0. % 0.10/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.10/0.31 % Computer : n019.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Jun 20 08:22:23 EDT 2024 % 0.10/0.31 % CPUTime : % 0.16/0.54 start to proof:theBenchmark % 76.13/76.70 %------------------------------------------- % 76.13/76.70 % File :CSE---1.7 % 76.13/76.70 % Problem :theBenchmark % 76.13/76.70 % Transform :cnf % 76.13/76.70 % Format :tptp:raw % 76.13/76.70 % Command :java -jar mcs_scs.jar %d %s % 76.13/76.70 % 76.13/76.70 % Result :Theorem 75.650000s % 76.13/76.70 % Output :CNFRefutation 75.650000s % 76.13/76.70 %------------------------------------------- % 76.13/76.71 %-------------------------------------------------------------------------- % 76.13/76.71 % File : GRP132-1.002 : TPTP v8.2.0. Released v1.2.0. % 76.13/76.71 % Domain : Group Theory (Quasigroups) % 76.13/76.71 % Problem : (3,1,2) conjugate orthogonality, no idempotence % 76.13/76.71 % Version : [Sla93] axioms. % 76.13/76.71 % English : Generate the multiplication table for the specified quasi- % 76.13/76.71 % group with 2 elements. % 76.13/76.71 % 76.13/76.71 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res % 76.13/76.71 % : [Sla93] Slaney (1993), Email to G. Sutcliffe % 76.13/76.71 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti % 76.13/76.71 % Source : [Sla93] % 76.13/76.71 % Names : QG2-ni [Sla93] % 76.13/76.71 % 76.13/76.71 % Status : Unsatisfiable % 76.13/76.71 % Rating : 0.00 v2.1.0 % 76.13/76.71 % Syntax : Number of clauses : 10 ( 4 unt; 1 nHn; 10 RR) % 76.13/76.71 % Number of literals : 27 ( 0 equ; 18 neg) % 76.13/76.71 % Maximal clause size : 5 ( 2 avg) % 76.13/76.71 % Maximal term depth : 1 ( 1 avg) % 76.13/76.71 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty) % 76.13/76.71 % Number of functors : 2 ( 2 usr; 2 con; 0-0 aty) % 76.13/76.71 % Number of variables : 26 ( 0 sgn) % 76.13/76.71 % SPC : CNF_UNS_EPR_NEQ_NHN % 76.13/76.71 % 76.13/76.71 % Comments : Slaney's [1993] axiomatization has been modified for this. % 76.13/76.71 % : Substitution axioms are not needed, as any positive equality % 76.13/76.71 % literals should resolve on negative ones directly. % 76.13/76.71 % : As in GRP130-1, either one of qg2_1 or qg2_2 may be used, as % 76.13/76.71 % each implies the other in this scenario, with the help of % 76.13/76.71 % cancellation. The dependence cannot be proved, so both have % 76.13/76.71 % been left in here. % 76.13/76.71 % : tptp2X: -f tptp -s2 GRP132-1.g % 76.13/76.71 %-------------------------------------------------------------------------- % 76.13/76.71 cnf(element_1,axiom, % 76.13/76.71 group_element(e_1) ). % 76.13/76.71 % 76.13/76.71 cnf(element_2,axiom, % 76.13/76.71 group_element(e_2) ). % 76.13/76.71 % 76.13/76.71 cnf(e_1_is_not_e_2,axiom, % 76.13/76.71 ~ equalish(e_1,e_2) ). % 76.13/76.71 % 76.13/76.71 cnf(e_2_is_not_e_1,axiom, % 76.13/76.71 ~ equalish(e_2,e_1) ). % 76.13/76.71 % 76.13/76.71 cnf(product_total_function1,axiom, % 76.13/76.71 ( ~ group_element(X) % 76.13/76.71 | ~ group_element(Y) % 76.13/76.71 | product(X,Y,e_1) % 76.13/76.71 | product(X,Y,e_2) ) ). % 76.13/76.71 % 76.13/76.71 cnf(product_total_function2,axiom, % 76.13/76.71 ( ~ product(X,Y,W) % 76.13/76.71 | ~ product(X,Y,Z) % 76.13/76.71 | equalish(W,Z) ) ). % 76.13/76.71 % 76.13/76.71 cnf(product_right_cancellation,axiom, % 76.13/76.71 ( ~ product(X,W,Y) % 76.13/76.71 | ~ product(X,Z,Y) % 76.13/76.71 | equalish(W,Z) ) ). % 76.13/76.71 % 76.13/76.71 cnf(product_left_cancellation,axiom, % 76.13/76.71 ( ~ product(W,Y,X) % 76.13/76.71 | ~ product(Z,Y,X) % 76.13/76.71 | equalish(W,Z) ) ). % 76.13/76.71 % 76.13/76.71 cnf(qg2_1,negated_conjecture, % 76.13/76.71 ( ~ product(X1,Y1,Z1) % 76.13/76.71 | ~ product(X2,Y2,Z1) % 76.13/76.71 | ~ product(Z2,X1,Y1) % 76.13/76.71 | ~ product(Z2,X2,Y2) % 76.13/76.71 | equalish(X1,X2) ) ). % 76.13/76.71 % 76.13/76.71 cnf(qg2_2,negated_conjecture, % 76.13/76.71 ( ~ product(X1,Y1,Z1) % 76.13/76.71 | ~ product(X2,Y2,Z1) % 76.13/76.71 | ~ product(Z2,X1,Y1) % 76.13/76.71 | ~ product(Z2,X2,Y2) % 76.13/76.71 | equalish(Y1,Y2) ) ). % 76.13/76.71 % 76.13/76.71 %-------------------------------------------------------------------------- % 76.13/76.71 %------------------------------------------- % 76.13/76.71 % Proof found % 76.13/76.71 % SZS status Theorem for theBenchmark % 76.13/76.71 % SZS output start Proof % 76.13/76.72 %ClaNum:10(EqnAxiom:0) % 76.13/76.72 %VarNum:58(SingletonVarNum:26) % 76.13/76.72 %MaxLitNum:5 % 76.13/76.72 %MaxfuncDepth:0 % 76.13/76.72 %SharedTerms:6 % 76.13/76.72 %goalClause: 9 10 % 76.13/76.72 [1]P1(a1) % 76.13/76.72 [2]P1(a2) % 76.13/76.72 [3]~P2(a1,a2) % 76.13/76.72 [4]~P2(a2,a1) % 76.13/76.72 [6]~P3(x63,x64,x61)+P2(x61,x62)+~P3(x63,x64,x62) % 76.13/76.72 [7]~P3(x73,x71,x74)+P2(x71,x72)+~P3(x73,x72,x74) % 76.13/76.72 [8]~P3(x81,x83,x84)+P2(x81,x82)+~P3(x82,x83,x84) % 76.13/76.72 [5]~P1(x52)+~P1(x51)+P3(x51,x52,a2)+P3(x51,x52,a1) % 76.13/76.72 [9]~P3(x95,x91,x96)+P2(x91,x92)+~P3(x93,x94,x92)+~P3(x93,x95,x91)+~P3(x94,x92,x96) % 76.13/76.72 [10]~P3(x101,x105,x106)+P2(x101,x102)+~P3(x103,x102,x104)+~P3(x103,x101,x105)+~P3(x102,x104,x106) % 76.13/76.72 %EqnAxiom % 76.13/76.72 % 76.13/76.72 %------------------------------------------- % 76.24/76.76 cnf(64926,plain, % 76.24/76.76 (~P3(x649261,x649262,a2)+~P3(x649261,x649262,a1)), % 76.24/76.76 inference(scs_inference,[],[3,6])). % 76.24/76.76 cnf(64935,plain, % 76.24/76.76 (~P3(a1,x649351,x649352)+~P3(a2,x649351,x649352)), % 76.24/76.76 inference(scs_inference,[],[4,8])). % 76.24/76.76 cnf(64946,plain, % 76.24/76.76 (~P3(a1,a2,a1)+P3(a1,a1,a2)), % 76.24/76.76 inference(scs_inference,[],[1,3,5,9,7])). % 76.24/76.76 cnf(64950,plain, % 76.24/76.76 (~P3(a1,a2,x649501)+~P3(a2,x649501,a1)+P3(a1,a1,a2)), % 76.24/76.76 inference(scs_inference,[],[1,4,3,5,9,7,8,10])). % 76.24/76.76 cnf(64953,plain, % 76.24/76.76 (~P3(a1,a2,a2)+~P3(a2,x649531,a1)+~P3(a1,a2,x649531)), % 76.24/76.76 inference(scs_inference,[],[3,7,64950])). % 76.24/76.76 cnf(64954,plain, % 76.24/76.76 (P3(a2,a2,a1)+P3(a2,a2,a2)), % 76.24/76.76 inference(scs_inference,[],[2,5])). % 76.24/76.76 cnf(64961,plain, % 76.24/76.76 (~P3(x649611,a2,x649612)+~P3(a1,x649613,x649614)+~P3(a2,x649612,x649614)+~P3(x649611,a1,x649613)), % 76.24/76.76 inference(scs_inference,[],[4,10])). % 76.24/76.76 cnf(64979,plain, % 76.24/76.76 (P3(a1,a2,a1)+~P3(a2,a2,a1)), % 76.24/76.76 inference(scs_inference,[],[2,1,64953,5])). % 76.24/76.76 cnf(64980,plain, % 76.24/76.76 (~P3(a2,a2,a1)+~P3(a1,a2,a2)), % 76.24/76.76 inference(scs_inference,[],[64979,64926])). % 76.24/76.76 cnf(64981,plain, % 76.24/76.76 (P3(a2,a2,a2)+~P3(a1,a2,a2)), % 76.24/76.77 inference(scs_inference,[],[64980,64954])). % 76.24/76.77 cnf(64982,plain, % 76.24/76.77 (~P3(a1,a2,a2)), % 76.24/76.77 inference(scs_inference,[],[64981,64935])). % 76.24/76.77 cnf(69753,plain, % 76.24/76.77 (~P1(x697531)+P3(x697531,x697532,a1)+P3(x697531,x697532,a2)+~P1(x697532)), % 76.24/76.77 inference(rename_variables,[],[5])). % 76.24/76.77 cnf(69761,plain, % 76.24/76.77 (~P3(a2,a1,a1)), % 76.24/76.77 inference(scs_inference,[],[2,64982,1,3,4,5,64946,6,7,8,64961])). % 76.24/76.77 cnf(69767,plain, % 76.24/76.77 (~P3(a2,a1,a2)), % 76.24/76.77 inference(scs_inference,[],[2,64982,1,3,4,5,64946,6,7,8,64961,69753,9,64935])). % 76.24/76.77 cnf(69770,plain, % 76.24/76.77 ($false), % 76.24/76.77 inference(scs_inference,[],[2,69761,69767,1,5]), % 76.24/76.77 ['proof']). % 76.31/76.82 % SZS output end Proof % 76.31/76.82 % Total time :75.650000s %------------------------------------------------------------------------------