%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : RNG011-5 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n004.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 14:00:38 EDT 2024 % Result : Unsatisfiable 0.54s 0.59s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : RNG011-5 : TPTP v8.2.0. Released v1.0.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n004.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 : Tue Jun 18 14:39:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.51/0.58 %------------------------------------------- % 0.51/0.58 % File :CSE---1.7 % 0.51/0.58 % Problem :theBenchmark % 0.51/0.58 % Transform :cnf % 0.51/0.58 % Format :tptp:raw % 0.51/0.58 % Command :java -jar mcs_scs.jar %d %s % 0.51/0.59 % 0.51/0.59 % Result :Theorem 0.000000s % 0.51/0.59 % Output :CNFRefutation 0.000000s % 0.51/0.59 %------------------------------------------- % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 % File : RNG011-5 : TPTP v8.2.0. Released v1.0.0. % 0.54/0.59 % Domain : Ring Theory % 0.54/0.59 % Problem : In a right alternative ring (((X,X,Y)*X)*(X,X,Y)) = Add Id % 0.54/0.59 % Version : [Ove90] (equality) axioms : % 0.54/0.59 % Incomplete > Augmented > Incomplete. % 0.54/0.59 % English : % 0.54/0.59 % 0.54/0.59 % Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 % 0.54/0.59 % : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal % 0.54/0.59 % : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 % 0.54/0.59 % : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in % 0.54/0.59 % Source : [Ove90] % 0.54/0.59 % Names : CADE-11 Competition Eq-10 [Ove90] % 0.54/0.59 % : THEOREM EQ-10 [LM93] % 0.54/0.59 % : PROBLEM 10 [Zha93] % 0.54/0.59 % 0.54/0.59 % Status : Unsatisfiable % 0.54/0.59 % Rating : 0.00 v8.2.0, 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.00 v7.0.0, 0.05 v6.3.0, 0.00 v2.0.0 % 0.54/0.59 % Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 2 RR) % 0.54/0.59 % Number of literals : 22 ( 22 equ; 1 neg) % 0.54/0.59 % Maximal clause size : 1 ( 1 avg) % 0.54/0.59 % Maximal term depth : 5 ( 2 avg) % 0.54/0.59 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.54/0.59 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty) % 0.54/0.59 % Number of variables : 37 ( 2 sgn) % 0.54/0.59 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.54/0.59 % 0.54/0.59 % Comments : % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 %----Commutativity of addition % 0.54/0.59 cnf(commutative_addition,axiom, % 0.54/0.59 add(X,Y) = add(Y,X) ). % 0.54/0.59 % 0.54/0.59 %----Associativity of addition % 0.54/0.59 cnf(associative_addition,axiom, % 0.54/0.59 add(add(X,Y),Z) = add(X,add(Y,Z)) ). % 0.54/0.59 % 0.54/0.59 %----Additive identity % 0.54/0.59 cnf(right_identity,axiom, % 0.54/0.59 add(X,additive_identity) = X ). % 0.54/0.59 % 0.54/0.59 cnf(left_identity,axiom, % 0.54/0.59 add(additive_identity,X) = X ). % 0.54/0.59 % 0.54/0.59 %----Additive inverse % 0.54/0.59 cnf(right_additive_inverse,axiom, % 0.54/0.59 add(X,additive_inverse(X)) = additive_identity ). % 0.54/0.59 % 0.54/0.59 cnf(left_additive_inverse,axiom, % 0.54/0.59 add(additive_inverse(X),X) = additive_identity ). % 0.54/0.59 % 0.54/0.59 %----Inverse of identity is identity, stupid % 0.54/0.59 cnf(additive_inverse_identity,axiom, % 0.54/0.59 additive_inverse(additive_identity) = additive_identity ). % 0.54/0.59 % 0.54/0.59 %----Axiom of Overbeek % 0.54/0.59 cnf(property_of_inverse_and_add,axiom, % 0.54/0.59 add(X,add(additive_inverse(X),Y)) = Y ). % 0.54/0.59 % 0.54/0.59 %----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y), % 0.54/0.59 cnf(distribute_additive_inverse,axiom, % 0.54/0.59 additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ). % 0.54/0.59 % 0.54/0.59 %----Inverse of additive_inverse of X is X % 0.54/0.59 cnf(additive_inverse_additive_inverse,axiom, % 0.54/0.59 additive_inverse(additive_inverse(X)) = X ). % 0.54/0.59 % 0.54/0.59 %----Behavior of 0 and the multiplication operation % 0.54/0.59 cnf(multiply_additive_id1,axiom, % 0.54/0.59 multiply(X,additive_identity) = additive_identity ). % 0.54/0.59 % 0.54/0.59 cnf(multiply_additive_id2,axiom, % 0.54/0.59 multiply(additive_identity,X) = additive_identity ). % 0.54/0.59 % 0.54/0.59 %----Axiom of Overbeek % 0.54/0.59 cnf(product_of_inverse,axiom, % 0.54/0.59 multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y) ). % 0.54/0.59 % 0.54/0.59 %----x * additive_inverse(y) = additive_inverse (x * y), % 0.54/0.59 cnf(multiply_additive_inverse1,axiom, % 0.54/0.59 multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ). % 0.54/0.59 % 0.54/0.59 cnf(multiply_additive_inverse2,axiom, % 0.54/0.59 multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ). % 0.54/0.59 % 0.54/0.59 %----Distributive property of product over sum % 0.54/0.59 cnf(distribute1,axiom, % 0.54/0.59 multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ). % 0.54/0.59 % 0.54/0.59 cnf(distribute2,axiom, % 0.54/0.59 multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ). % 0.54/0.59 % 0.54/0.59 %----Right alternative law % 0.54/0.59 cnf(right_alternative,axiom, % 0.54/0.59 multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ). % 0.54/0.59 % 0.54/0.59 %----Associator % 0.54/0.59 cnf(associator,axiom, % 0.54/0.59 associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ). % 0.54/0.59 % 0.54/0.59 %----Commutator % 0.54/0.59 cnf(commutator,axiom, % 0.54/0.59 commutator(X,Y) = add(multiply(Y,X),additive_inverse(multiply(X,Y))) ). % 0.54/0.59 % 0.54/0.59 %----Middle associator identity % 0.54/0.59 cnf(middle_associator,axiom, % 0.54/0.59 multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ). % 0.54/0.59 % 0.54/0.59 cnf(prove_equality,negated_conjecture, % 0.54/0.59 multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity ). % 0.54/0.59 % 0.54/0.59 %-------------------------------------------------------------------------- % 0.54/0.59 %------------------------------------------- % 0.54/0.59 % Proof found % 0.54/0.59 % SZS status Theorem for theBenchmark % 0.54/0.59 % SZS output start Proof % 0.54/0.59 %ClaNum:28(EqnAxiom:8) % 0.54/0.59 %VarNum:75(SingletonVarNum:32) % 0.54/0.59 %MaxLitNum:1 % 0.54/0.59 %MaxfuncDepth:5 % 0.54/0.59 %SharedTerms:14 % 0.54/0.59 %goalClause: 28 % 0.54/0.59 %singleGoalClaCount:1 % 0.54/0.59 [9]E(f4(a1),a1) % 0.54/0.59 [28]~E(f5(f5(f2(f5(f5(a3,a3),a6),f4(f5(a3,f5(a3,a6)))),a3),f2(f5(f5(a3,a3),a6),f4(f5(a3,f5(a3,a6))))),a1) % 0.54/0.59 [11]E(f5(x111,a1),a1) % 0.54/0.59 [12]E(f5(a1,x121),a1) % 0.54/0.59 [13]E(f2(x131,a1),x131) % 0.54/0.59 [14]E(f2(a1,x141),x141) % 0.54/0.59 [10]E(f4(f4(x101)),x101) % 0.54/0.59 [15]E(f2(x151,f4(x151)),a1) % 0.54/0.59 [16]E(f2(f4(x161),x161),a1) % 0.54/0.59 [17]E(f2(x171,x172),f2(x172,x171)) % 0.54/0.59 [18]E(f5(f4(x181),f4(x182)),f5(x181,x182)) % 0.54/0.59 [19]E(f4(f5(x191,x192)),f5(x191,f4(x192))) % 0.54/0.59 [20]E(f4(f5(x201,x202)),f5(f4(x201),x202)) % 0.54/0.59 [22]E(f4(f2(x221,x222)),f2(f4(x221),f4(x222))) % 0.54/0.59 [24]E(f5(f5(x241,x242),x242),f5(x241,f5(x242,x242))) % 0.54/0.59 [21]E(f2(x211,f2(f4(x211),x212)),x212) % 0.54/0.59 [27]E(f5(f5(f2(f5(f5(x271,x271),x272),f4(f5(x271,f5(x271,x272)))),x271),f2(f5(f5(x271,x271),x272),f4(f5(x271,f5(x271,x272))))),a1) % 0.54/0.59 [23]E(f2(f2(x231,x232),x233),f2(x231,f2(x232,x233))) % 0.54/0.60 [25]E(f2(f5(x251,x252),f5(x251,x253)),f5(x251,f2(x252,x253))) % 0.54/0.60 [26]E(f2(f5(x261,x262),f5(x263,x262)),f5(f2(x261,x263),x262)) % 0.54/0.60 %EqnAxiom % 0.54/0.60 [1]E(x11,x11) % 0.54/0.60 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.60 [4]~E(x41,x42)+E(f4(x41),f4(x42)) % 0.54/0.60 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53)) % 0.54/0.60 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62)) % 0.54/0.60 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73)) % 0.54/0.60 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82)) % 0.54/0.60 % 0.54/0.60 %------------------------------------------- % 0.54/0.60 cnf(29,plain, % 0.54/0.60 ($false), % 0.54/0.60 inference(scs_inference,[],[28,27]), % 0.54/0.60 ['proof']). % 0.54/0.60 % SZS output end Proof % 0.54/0.60 % Total time :0.000000s %------------------------------------------------------------------------------