%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD010-1 : TPTP v8.1.0. Bugfixed v2.7.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n028.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 : 600s % DateTime : Sat Jul 16 02:28:15 EDT 2022 % Result : Unsatisfiable 0.19s 0.41s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : FLD010-1 : TPTP v8.1.0. Bugfixed v2.7.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jun 7 00:36:29 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.41 % 0.19/0.41 SPASS V 3.9 % 0.19/0.41 SPASS beiseite: Proof found. % 0.19/0.41 % SZS status Theorem % 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.41 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses. % 0.19/0.41 SPASS allocated 75694 KBytes. % 0.19/0.41 SPASS spent 0:00:00.06 on the problem. % 0.19/0.41 0:00:00.03 for the input. % 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.41 0:00:00.00 for inferences. % 0.19/0.41 0:00:00.00 for the backtracking. % 0.19/0.41 0:00:00.01 for the reduction. % 0.19/0.41 % 0.19/0.41 % 0.19/0.41 Here is a proof with depth 4, length 17 : % 0.19/0.41 % SZS output start Refutation % 0.19/0.41 1[0:Inp] || equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)*l -> . % 0.19/0.41 7[0:Inp] defined(u) || -> equalish(multiply(multiplicative_identity,u),u)*l. % 0.19/0.41 8[0:Inp] defined(u) || -> equalish(u,additive_identity) equalish(multiply(u,multiplicative_inverse(u)),multiplicative_identity)*l. % 0.19/0.41 15[0:Inp] || -> defined(multiplicative_identity)*. % 0.19/0.41 16[0:Inp] defined(u) || -> defined(multiplicative_inverse(u))* equalish(u,additive_identity). % 0.19/0.41 23[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.19/0.41 24[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.19/0.41 28[0:Inp] || equalish(additive_identity,multiplicative_identity)*r -> . % 0.19/0.41 38[0:Res:7.1,23.0] defined(u) || -> equalish(u,multiply(multiplicative_identity,u))*r. % 0.19/0.41 107[0:OCh:24.1,24.0,8.2,38.1] defined(multiplicative_identity) defined(multiplicative_inverse(multiplicative_identity)) || -> equalish(multiplicative_identity,additive_identity) equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)*l. % 0.19/0.41 109[0:SSi:107.0,15.0] defined(multiplicative_inverse(multiplicative_identity)) || -> equalish(multiplicative_identity,additive_identity) equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity)*l. % 0.19/0.41 110[0:MRR:109.2,1.0] defined(multiplicative_inverse(multiplicative_identity)) || -> equalish(multiplicative_identity,additive_identity)*l. % 0.19/0.41 111[0:SoR:110.0,16.1] defined(multiplicative_identity) || -> equalish(multiplicative_identity,additive_identity)*l equalish(multiplicative_identity,additive_identity)*l. % 0.19/0.41 112[0:Obv:111.1] defined(multiplicative_identity) || -> equalish(multiplicative_identity,additive_identity)*l. % 0.19/0.41 113[0:SSi:112.0,15.0] || -> equalish(multiplicative_identity,additive_identity)*l. % 0.19/0.41 114[0:Res:113.0,23.0] || -> equalish(additive_identity,multiplicative_identity)*r. % 0.19/0.41 116[0:MRR:114.0,28.0] || -> . % 0.19/0.41 % SZS output end Refutation % 0.19/0.41 Formulae used in the proof : multiplicative_inv_not_equal_to_multiplicative_id_2 existence_of_identity_multiplication existence_of_inverse_multiplication well_definedness_of_multiplicative_identity well_definedness_of_multiplicative_inverse symmetry_of_equality transitivity_of_equality different_identities % 0.19/0.41 %------------------------------------------------------------------------------