%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP124-2.004 : 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 : n022.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 06:38:48 EDT 2024 % Result : Unsatisfiable 58.68s 58.85s % Output : CNFRefutation 58.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GRP124-2.004 : 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 % 0.15/0.36 % Computer : n022.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Jun 20 11:52:09 EDT 2024 % 0.15/0.36 % CPUTime : % 0.57/0.62 start to proof:theBenchmark % 58.68/58.83 %------------------------------------------- % 58.68/58.83 % File :CSE---1.7 % 58.68/58.83 % Problem :theBenchmark % 58.68/58.83 % Transform :cnf % 58.68/58.83 % Format :tptp:raw % 58.68/58.83 % Command :java -jar mcs_scs.jar %d %s % 58.68/58.83 % 58.68/58.83 % Result :Theorem 58.020000s % 58.68/58.83 % Output :CNFRefutation 58.020000s % 58.68/58.83 %------------------------------------------- % 58.68/58.85 %-------------------------------------------------------------------------- % 58.68/58.85 % File : GRP124-2.004 : TPTP v8.2.0. Released v1.2.0. % 58.68/58.85 % Domain : Group Theory (Quasigroups) % 58.68/58.85 % Problem : (3,1,2) conjugate orthogonality % 58.68/58.85 % Version : [Sla93] axioms : Augmented. % 58.68/58.85 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c. % 58.68/58.85 % Generate the multiplication table for the specified quasi- % 58.68/58.85 % group with 4 elements. % 58.68/58.85 % 58.68/58.85 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res % 58.68/58.85 % : [Sla93] Slaney (1993), Email to G. Sutcliffe % 58.68/58.85 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti % 58.68/58.85 % Source : [TPTP] % 58.68/58.85 % Names : % 58.68/58.85 % 58.68/58.85 % Status : Unsatisfiable % 58.68/58.85 % Rating : 0.00 v2.1.0 % 58.68/58.85 % Syntax : Number of clauses : 33 ( 26 unt; 1 nHn; 32 RR) % 58.68/58.85 % Number of literals : 54 ( 0 equ; 31 neg) % 58.68/58.85 % Maximal clause size : 6 ( 1 avg) % 58.68/58.85 % Maximal term depth : 1 ( 1 avg) % 58.68/58.85 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty) % 58.68/58.85 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 58.68/58.85 % Number of variables : 30 ( 0 sgn) % 58.68/58.85 % SPC : CNF_UNS_EPR_NEQ_NHN % 58.68/58.85 % 58.68/58.85 % Comments : [SFS93]'s axiomatization has been modified for this. % 58.68/58.85 % : Substitution axioms are not needed, as any positive equality % 58.68/58.85 % literals should resolve on negative ones directly. % 58.68/58.85 % : As in GRP123-1, either one of qg2_1 or qg2_2 may be used, as % 58.68/58.85 % each implies the other in this scenario, with the help of % 58.68/58.85 % cancellation. The dependence cannot be proved, so both have % 58.68/58.85 % been left in here. % 58.68/58.85 % : Version 2 has simple isomorphism avoidance (as mentioned in % 58.68/58.85 % [FSB93]) % 58.68/58.85 % : tptp2X: -f tptp -s4 GRP124-2.g % 58.68/58.85 %-------------------------------------------------------------------------- % 58.68/58.85 cnf(e_1_then_e_2,axiom, % 58.68/58.85 next(e_1,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_2_then_e_3,axiom, % 58.68/58.85 next(e_2,e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_then_e_4,axiom, % 58.68/58.85 next(e_3,e_4) ). % 58.68/58.85 % 58.68/58.85 cnf(e_2_greater_e_1,axiom, % 58.68/58.85 greater(e_2,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_greater_e_1,axiom, % 58.68/58.85 greater(e_3,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_greater_e_1,axiom, % 58.68/58.85 greater(e_4,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_greater_e_2,axiom, % 58.68/58.85 greater(e_3,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_greater_e_2,axiom, % 58.68/58.85 greater(e_4,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_greater_e_3,axiom, % 58.68/58.85 greater(e_4,e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(no_redundancy,axiom, % 58.68/58.85 ( ~ product(X,e_1,Y) % 58.68/58.85 | ~ next(X,X1) % 58.68/58.85 | ~ greater(Y,X1) ) ). % 58.68/58.85 % 58.68/58.85 cnf(element_1,axiom, % 58.68/58.85 group_element(e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(element_2,axiom, % 58.68/58.85 group_element(e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(element_3,axiom, % 58.68/58.85 group_element(e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(element_4,axiom, % 58.68/58.85 group_element(e_4) ). % 58.68/58.85 % 58.68/58.85 cnf(e_1_is_not_e_2,axiom, % 58.68/58.85 ~ equalish(e_1,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_1_is_not_e_3,axiom, % 58.68/58.85 ~ equalish(e_1,e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(e_1_is_not_e_4,axiom, % 58.68/58.85 ~ equalish(e_1,e_4) ). % 58.68/58.85 % 58.68/58.85 cnf(e_2_is_not_e_1,axiom, % 58.68/58.85 ~ equalish(e_2,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_2_is_not_e_3,axiom, % 58.68/58.85 ~ equalish(e_2,e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(e_2_is_not_e_4,axiom, % 58.68/58.85 ~ equalish(e_2,e_4) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_is_not_e_1,axiom, % 58.68/58.85 ~ equalish(e_3,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_is_not_e_2,axiom, % 58.68/58.85 ~ equalish(e_3,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_3_is_not_e_4,axiom, % 58.68/58.85 ~ equalish(e_3,e_4) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_is_not_e_1,axiom, % 58.68/58.85 ~ equalish(e_4,e_1) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_is_not_e_2,axiom, % 58.68/58.85 ~ equalish(e_4,e_2) ). % 58.68/58.85 % 58.68/58.85 cnf(e_4_is_not_e_3,axiom, % 58.68/58.85 ~ equalish(e_4,e_3) ). % 58.68/58.85 % 58.68/58.85 cnf(product_total_function1,axiom, % 58.68/58.85 ( ~ group_element(X) % 58.68/58.85 | ~ group_element(Y) % 58.68/58.85 | product(X,Y,e_1) % 58.68/58.85 | product(X,Y,e_2) % 58.68/58.85 | product(X,Y,e_3) % 58.68/58.85 | product(X,Y,e_4) ) ). % 58.68/58.85 % 58.68/58.85 cnf(product_total_function2,axiom, % 58.68/58.85 ( ~ product(X,Y,W) % 58.68/58.85 | ~ product(X,Y,Z) % 58.68/58.85 | equalish(W,Z) ) ). % 58.68/58.85 % 58.68/58.85 cnf(product_right_cancellation,axiom, % 58.68/58.85 ( ~ product(X,W,Y) % 58.68/58.85 | ~ product(X,Z,Y) % 58.68/58.85 | equalish(W,Z) ) ). % 58.68/58.85 % 58.68/58.85 cnf(product_left_cancellation,axiom, % 58.68/58.85 ( ~ product(W,Y,X) % 58.68/58.85 | ~ product(Z,Y,X) % 58.68/58.85 | equalish(W,Z) ) ). % 58.68/58.85 % 58.68/58.85 cnf(product_idempotence,axiom, % 58.68/58.85 product(X,X,X) ). % 58.68/58.85 % 58.68/58.85 cnf(qg2_1,negated_conjecture, % 58.68/58.85 ( ~ product(X1,Y1,Z1) % 58.68/58.85 | ~ product(X2,Y2,Z1) % 58.68/58.85 | ~ product(Z2,X1,Y1) % 58.68/58.85 | ~ product(Z2,X2,Y2) % 58.68/58.85 | equalish(X1,X2) ) ). % 58.68/58.85 % 58.68/58.85 cnf(qg2_2,negated_conjecture, % 58.68/58.85 ( ~ product(X1,Y1,Z1) % 58.68/58.85 | ~ product(X2,Y2,Z1) % 58.68/58.85 | ~ product(Z2,X1,Y1) % 58.68/58.85 | ~ product(Z2,X2,Y2) % 58.68/58.85 | equalish(Y1,Y2) ) ). % 58.68/58.85 % 58.68/58.85 %-------------------------------------------------------------------------- % 58.68/58.85 %------------------------------------------- % 58.68/58.85 % Proof found % 58.68/58.85 % SZS status Theorem for theBenchmark % 58.68/58.85 % SZS output start Proof % 58.68/58.86 %ClaNum:33(EqnAxiom:0) % 58.68/58.86 %VarNum:71(SingletonVarNum:30) % 58.68/58.86 %MaxLitNum:6 % 58.68/58.86 %MaxfuncDepth:0 % 58.68/58.86 %SharedTerms:29 % 58.68/58.86 %goalClause: 32 33 % 58.68/58.86 [1]P1(a1) % 58.68/58.86 [2]P1(a2) % 58.68/58.86 [3]P1(a3) % 58.68/58.86 [4]P1(a4) % 58.68/58.86 [5]P4(a1,a2) % 58.68/58.86 [6]P4(a2,a3) % 58.68/58.86 [7]P4(a3,a4) % 58.68/58.86 [8]P2(a2,a1) % 58.68/58.86 [9]P2(a3,a1) % 58.68/58.86 [10]P2(a3,a2) % 58.68/58.86 [11]P2(a4,a1) % 58.68/58.86 [12]P2(a4,a2) % 58.68/58.86 [13]P2(a4,a3) % 58.68/58.86 [15]~P3(a1,a2) % 58.68/58.86 [16]~P3(a1,a3) % 58.68/58.86 [17]~P3(a1,a4) % 58.68/58.86 [18]~P3(a2,a1) % 58.68/58.86 [19]~P3(a2,a3) % 58.68/58.86 [20]~P3(a2,a4) % 58.68/58.86 [21]~P3(a3,a1) % 58.68/58.86 [22]~P3(a3,a2) % 58.68/58.86 [23]~P3(a3,a4) % 58.68/58.86 [24]~P3(a4,a1) % 58.68/58.86 [25]~P3(a4,a2) % 58.68/58.86 [26]~P3(a4,a3) % 58.68/58.86 [14]P5(x141,x141,x141) % 58.68/58.86 [27]~P4(x271,x272)+~P2(x273,x272)+~P5(x271,a1,x273) % 58.68/58.86 [28]~P5(x283,x284,x281)+P3(x281,x282)+~P5(x283,x284,x282) % 58.68/58.86 [29]~P5(x293,x291,x294)+P3(x291,x292)+~P5(x293,x292,x294) % 58.68/58.86 [30]~P5(x301,x303,x304)+P3(x301,x302)+~P5(x302,x303,x304) % 58.68/58.86 [32]~P5(x325,x321,x326)+P3(x321,x322)+~P5(x323,x324,x322)+~P5(x323,x325,x321)+~P5(x324,x322,x326) % 58.68/58.86 [33]~P5(x331,x335,x336)+P3(x331,x332)+~P5(x333,x332,x334)+~P5(x333,x331,x335)+~P5(x332,x334,x336) % 58.68/58.86 [31]~P1(x312)+~P1(x311)+P5(x311,x312,a2)+P5(x311,x312,a3)+P5(x311,x312,a4)+P5(x311,x312,a1) % 58.68/58.86 %EqnAxiom % 58.68/58.86 % 58.68/58.86 %------------------------------------------- % 58.88/59.06 cnf(323725,plain, % 58.88/59.06 (P5(x3237251,x3237251,x3237251)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323727,plain, % 58.88/59.06 (~P5(a2,a1,a1)), % 58.88/59.06 inference(scs_inference,[],[15,14,323725,29,30])). % 58.88/59.06 cnf(323728,plain, % 58.88/59.06 (P5(x3237281,x3237281,x3237281)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323731,plain, % 58.88/59.06 (P5(x3237311,x3237311,x3237311)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323733,plain, % 58.88/59.06 (~P5(a2,a1,a4)), % 58.88/59.06 inference(scs_inference,[],[6,13,15,14,323725,323728,29,30,28,27])). % 58.88/59.06 cnf(323737,plain, % 58.88/59.06 (~P5(a2,x3237371,a1)+~P5(a1,a2,x3237371)), % 58.88/59.06 inference(scs_inference,[],[6,13,15,14,323725,323728,323731,29,30,28,27,32,33])). % 58.88/59.06 cnf(323740,plain, % 58.88/59.06 (~P5(a2,a4,a1)+P5(a1,a2,a2)+P5(a1,a2,a3)), % 58.88/59.06 inference(scs_inference,[],[1,2,6,13,15,14,323725,323728,323731,29,30,28,27,32,33,31])). % 58.88/59.06 cnf(323742,plain, % 58.88/59.06 (P5(x3237421,x3237421,x3237421)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323744,plain, % 58.88/59.06 (~P5(a1,a3,a1)), % 58.88/59.06 inference(scs_inference,[],[16,14,323742,30,29])). % 58.88/59.06 cnf(323780,plain, % 58.88/59.06 (P5(x3237801,x3237801,x3237801)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323782,plain, % 58.88/59.06 (~P5(a2,a3,a2)), % 58.88/59.06 inference(scs_inference,[],[19,14,323780,30,29])). % 58.88/59.06 cnf(323783,plain, % 58.88/59.06 (P5(x3237831,x3237831,x3237831)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323786,plain, % 58.88/59.06 (P5(x3237861,x3237861,x3237861)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323792,plain, % 58.88/59.06 (P5(a2,a1,a3)+P5(a2,a1,a2)), % 58.88/59.06 inference(scs_inference,[],[1,7,19,323733,323727,2,14,323780,323783,323786,30,29,28,33,27,31])). % 58.88/59.06 cnf(323794,plain, % 58.88/59.06 (~P5(a2,a4,a2)), % 58.88/59.06 inference(scs_inference,[],[20,14,29])). % 58.88/59.06 cnf(323808,plain, % 58.88/59.06 (~P5(a1,a3,a3)), % 58.88/59.06 inference(scs_inference,[],[21,14,30])). % 58.88/59.06 cnf(323809,plain, % 58.88/59.06 (P5(x3238091,x3238091,x3238091)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323812,plain, % 58.88/59.06 (P5(x3238121,x3238121,x3238121)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323815,plain, % 58.88/59.06 (P5(x3238151,x3238151,x3238151)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323821,plain, % 58.88/59.06 (~P5(a1,x3238211,a3)+~P5(x3238211,a3,a1)), % 58.88/59.06 inference(scs_inference,[],[21,7,14,323809,323812,323815,30,29,28,33,27,32])). % 58.88/59.06 cnf(323826,plain, % 58.88/59.06 (P5(x3238261,x3238261,x3238261)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323828,plain, % 58.88/59.06 (~P5(a2,a3,a3)), % 58.88/59.06 inference(scs_inference,[],[22,14,323826,29,30])). % 58.88/59.06 cnf(323876,plain, % 58.88/59.06 (~P5(a2,a4,a4)), % 58.88/59.06 inference(scs_inference,[],[25,14,30])). % 58.88/59.06 cnf(323910,plain, % 58.88/59.06 (P5(x3239101,x3239101,x3239101)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323913,plain, % 58.88/59.06 (P5(x3239131,x3239131,x3239131)), % 58.88/59.06 inference(rename_variables,[],[14])). % 58.88/59.06 cnf(323917,plain, % 58.88/59.06 (P5(a2,a1,a3)), % 58.88/59.06 inference(scs_inference,[],[18,14,323910,323913,30,29,32,323792])). % 58.88/59.06 cnf(323918,plain, % 58.88/59.06 (P5(a1,a2,a3)+~P5(a2,a4,a1)), % 58.88/59.06 inference(scs_inference,[],[18,14,323910,323913,30,29,32,323792,323740])). % 58.88/59.06 cnf(323922,plain, % 58.88/59.06 (P5(a1,a3,a4)), % 58.88/59.06 inference(scs_inference,[],[1,323808,323744,18,3,14,323910,323913,30,29,32,323792,323740,33,31])). % 58.88/59.06 cnf(323940,plain, % 58.88/59.06 (P5(a1,a2,a3)), % 58.88/59.06 inference(scs_inference,[],[323917,323794,323876,323922,4,9,17,2,14,27,29,33,32,31,323918])). % 58.88/59.06 cnf(323943,plain, % 58.88/59.06 (~P5(a2,a3,a4)), % 58.88/59.06 inference(scs_inference,[],[323917,323794,323876,323922,4,9,17,2,15,14,27,29,33,32,31,323918,323737,30])). % 58.88/59.06 cnf(323946,plain, % 58.88/59.06 ($false), % 58.88/59.06 inference(scs_inference,[],[323940,2,323943,3,323828,323782,323821,31]), % 58.88/59.06 ['proof']). % 58.99/59.20 % SZS output end Proof % 58.99/59.20 % Total time :58.020000s %------------------------------------------------------------------------------