%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP006-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n020.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 06:38:25 EDT 2024 % Result : Unsatisfiable 0.53s 0.61s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP006-1 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n020.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 11:19:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.53/0.56 start to proof:theBenchmark % 0.53/0.60 %------------------------------------------- % 0.53/0.60 % File :CSE---1.7 % 0.53/0.60 % Problem :theBenchmark % 0.53/0.60 % Transform :cnf % 0.53/0.60 % Format :tptp:raw % 0.53/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.60 % 0.53/0.60 % Result :Theorem 0.000000s % 0.53/0.60 % Output :CNFRefutation 0.000000s % 0.53/0.60 %------------------------------------------- % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 % File : GRP006-1 : TPTP v8.2.0. Released v1.0.0. % 0.53/0.60 % Domain : Group Theory % 0.53/0.60 % Problem : Inverse is in this group % 0.53/0.60 % Version : [Cha70] axioms : Incomplete. % 0.53/0.60 % English : If S is a non-empty subset of a group such that if X, Y belong % 0.53/0.60 % to S, the XY^-1 belongs to S, then S contains X^-1 whenever it % 0.53/0.60 % contains X. % 0.53/0.60 % 0.53/0.60 % Refs : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th % 0.53/0.60 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo % 0.53/0.60 % Source : [Cha70] % 0.53/0.60 % Names : Example 6 [Cha70] % 0.53/0.60 % : Example 6 [CL73] % 0.53/0.60 % : EX6 [SPRFN] % 0.53/0.60 % 0.53/0.60 % Status : Unsatisfiable % 0.53/0.60 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.0.0 % 0.53/0.60 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 5 RR) % 0.53/0.60 % Number of literals : 18 ( 0 equ; 10 neg) % 0.53/0.60 % Maximal clause size : 4 ( 2 avg) % 0.53/0.60 % Maximal term depth : 2 ( 1 avg) % 0.53/0.60 % Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty) % 0.53/0.60 % Number of functors : 3 ( 3 usr; 2 con; 0-1 aty) % 0.53/0.60 % Number of variables : 19 ( 0 sgn) % 0.53/0.60 % SPC : CNF_UNS_RFO_NEQ_HRN % 0.53/0.60 % 0.53/0.60 % Comments : % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 cnf(left_identity,axiom, % 0.53/0.60 product(identity,X,X) ). % 0.53/0.60 % 0.53/0.60 cnf(right_identity,axiom, % 0.53/0.60 product(X,identity,X) ). % 0.53/0.60 % 0.53/0.60 cnf(right_inverse,axiom, % 0.53/0.60 product(X,inverse(X),identity) ). % 0.53/0.60 % 0.53/0.60 cnf(left_inverse,axiom, % 0.53/0.60 product(inverse(X),X,identity) ). % 0.53/0.60 % 0.53/0.61 cnf(condition,axiom, % 0.53/0.61 ( ~ an_element(X) % 0.53/0.61 | ~ an_element(Y) % 0.53/0.61 | ~ product(X,inverse(Y),Z) % 0.53/0.61 | an_element(Z) ) ). % 0.53/0.61 % 0.53/0.61 cnf(associativity1,axiom, % 0.53/0.61 ( ~ product(X,Y,U) % 0.53/0.61 | ~ product(Y,Z,V) % 0.53/0.61 | ~ product(U,Z,W) % 0.53/0.61 | product(X,V,W) ) ). % 0.53/0.61 % 0.53/0.61 cnf(associativity2,axiom, % 0.53/0.61 ( ~ product(X,Y,U) % 0.53/0.61 | ~ product(Y,Z,V) % 0.53/0.61 | ~ product(X,V,W) % 0.53/0.61 | product(U,Z,W) ) ). % 0.53/0.61 % 0.53/0.61 cnf(element_of_set,hypothesis, % 0.53/0.61 an_element(the_element) ). % 0.53/0.61 % 0.53/0.61 cnf(prove_b_inverse_is_in_set,negated_conjecture, % 0.53/0.61 ~ an_element(inverse(the_element)) ). % 0.53/0.61 % 0.53/0.61 %-------------------------------------------------------------------------- % 0.53/0.61 %------------------------------------------- % 0.53/0.61 % Proof found % 0.53/0.61 % SZS status Theorem for theBenchmark % 0.53/0.61 % SZS output start Proof % 0.53/0.61 %ClaNum:9(EqnAxiom:0) % 0.53/0.61 %VarNum:38(SingletonVarNum:19) % 0.53/0.61 %MaxLitNum:4 % 0.53/0.61 %MaxfuncDepth:1 % 0.53/0.61 %SharedTerms:5 % 0.53/0.61 %goalClause: 6 % 0.53/0.61 %singleGoalClaCount:1 % 0.53/0.61 [1]P1(a1) % 0.53/0.61 [6]~P1(f3(a1)) % 0.53/0.61 [2]P2(x21,a2,x21) % 0.53/0.61 [3]P2(a2,x31,x31) % 0.53/0.61 [4]P2(x41,f3(x41),a2) % 0.53/0.61 [5]P2(f3(x51),x51,a2) % 0.53/0.61 [7]P1(x71)+~P1(x72)+~P1(x73)+~P2(x73,f3(x72),x71) % 0.53/0.61 [8]~P2(x86,x84,x81)+P2(x81,x82,x83)+~P2(x84,x82,x85)+~P2(x86,x85,x83) % 0.53/0.61 [9]~P2(x91,x96,x94)+P2(x91,x92,x93)+~P2(x94,x95,x93)+~P2(x96,x95,x92) % 0.53/0.61 %EqnAxiom % 0.53/0.61 % 0.53/0.61 %------------------------------------------- % 0.53/0.61 cnf(10,plain, % 0.53/0.61 (~P1(a2)), % 0.53/0.61 inference(scs_inference,[],[6,1,3,7])). % 0.53/0.61 cnf(17,plain, % 0.53/0.61 (P2(f3(x171),x171,a2)), % 0.53/0.61 inference(rename_variables,[],[5])). % 0.53/0.61 cnf(20,plain, % 0.53/0.61 (P2(f3(x201),x201,a2)), % 0.53/0.61 inference(rename_variables,[],[5])). % 0.53/0.61 cnf(22,plain, % 0.53/0.61 (P2(a2,f3(f3(a2)),a2)), % 0.53/0.61 inference(scs_inference,[],[10,1,5,17,20,3,4,9,7,8])). % 0.53/0.61 cnf(28,plain, % 0.53/0.61 (P2(x281,f3(x281),a2)), % 0.53/0.61 inference(rename_variables,[],[4])). % 0.53/0.61 cnf(31,plain, % 0.53/0.61 ($false), % 0.53/0.61 inference(scs_inference,[],[10,1,5,22,4,28,9,7]), % 0.53/0.61 ['proof']). % 0.53/0.61 % SZS output end Proof % 0.53/0.61 % Total time :0.000000s %------------------------------------------------------------------------------