%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD037-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n025.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 02:28:25 EDT 2022 % Result : Unsatisfiable 0.19s 0.43s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : FLD037-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.06/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n025.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 : 600 % 0.12/0.33 % DateTime : Mon Jun 6 13:59:33 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.43 % 0.19/0.43 SPASS V 3.9 % 0.19/0.43 SPASS beiseite: Proof found. % 0.19/0.43 % SZS status Theorem % 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.43 SPASS derived 135 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses. % 0.19/0.43 SPASS allocated 75801 KBytes. % 0.19/0.43 SPASS spent 0:00:00.08 on the problem. % 0.19/0.43 0:00:00.03 for the input. % 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.43 0:00:00.00 for inferences. % 0.19/0.43 0:00:00.00 for the backtracking. % 0.19/0.43 0:00:00.02 for the reduction. % 0.19/0.43 % 0.19/0.43 % 0.19/0.43 Here is a proof with depth 3, length 18 : % 0.19/0.43 % SZS output start Refutation % 0.19/0.43 1[0:Inp] || -> defined(a)*. % 0.19/0.43 3[0:Inp] || equalish(a,additive_identity)*l -> . % 0.19/0.43 4[0:Inp] || -> equalish(a,b)*l. % 0.19/0.43 5[0:Inp] || equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a)))*r -> . % 0.19/0.43 12[0:Inp] defined(u) || -> equalish(u,additive_identity) equalish(multiply(u,multiplicative_inverse(u)),multiplicative_identity)*l. % 0.19/0.43 20[0:Inp] defined(u) || -> defined(multiplicative_inverse(u))* equalish(u,additive_identity). % 0.19/0.43 27[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.19/0.43 28[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.19/0.43 30[0:Inp] defined(u) || equalish(v,w) -> equalish(multiply(v,u),multiply(w,u))*. % 0.19/0.43 34[0:Res:4.0,30.1] defined(u) || -> equalish(multiply(a,u),multiply(b,u))*l. % 0.19/0.43 38[0:Res:12.2,3.0] defined(a) || -> equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)*l. % 0.19/0.43 39[0:Res:20.2,3.0] defined(a) || -> defined(multiplicative_inverse(a))*. % 0.19/0.43 43[0:MRR:39.0,1.0] || -> defined(multiplicative_inverse(a))*. % 0.19/0.43 44[0:MRR:38.0,1.0] || -> equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)*l. % 0.19/0.43 60[0:Res:44.0,27.0] || -> equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a)))*r. % 0.19/0.43 220[0:OCh:28.1,28.0,34.1,60.0] defined(multiplicative_inverse(a)) || -> equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a)))*r. % 0.19/0.43 223[0:SSi:220.0,43.0] || -> equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a)))*r. % 0.19/0.43 224[0:MRR:223.0,5.0] || -> . % 0.19/0.43 % SZS output end Refutation % 0.19/0.43 Formulae used in the proof : a_is_defined a_not_equal_to_additive_identity_3 a_equals_b_4 multiplicative_identity_not_equal_to_multiply_5 existence_of_inverse_multiplication well_definedness_of_multiplicative_inverse symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_multiplication % 0.19/0.43 %------------------------------------------------------------------------------