%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD006-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n021.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 02:28:13 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 % 0.00/0.12 % Problem : FLD006-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.12/0.12 % Command : run_spass %d %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 6 18:41:05 EDT 2022 % 0.12/0.34 % 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/sandbox/benchmark/theBenchmark.p % 0.19/0.41 SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 42 clauses. % 0.19/0.41 SPASS allocated 75658 KBytes. % 0.19/0.41 SPASS spent 0:00:00.06 on the problem. % 0.19/0.41 0:00:00.04 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 0:00:00.00 for the reduction. % 0.19/0.41 % 0.19/0.41 % 0.19/0.41 Here is a proof with depth 2, length 11 : % 0.19/0.41 % SZS output start Refutation % 0.19/0.41 1[0:Inp] || equalish(additive_inverse(additive_identity),additive_identity)*l -> . % 0.19/0.41 3[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 0.19/0.41 4[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 0.19/0.41 12[0:Inp] || -> defined(additive_identity)*. % 0.19/0.41 13[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 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 42[0:Res:3.1,23.0] defined(u) || -> equalish(u,add(additive_identity,u))*r. % 0.19/0.41 64[0:OCh:24.1,24.0,42.1,4.1] defined(additive_inverse(additive_identity)) defined(additive_identity) || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 0.19/0.41 68[0:SSi:64.1,64.0,12.0,13.1,12.0] || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 0.19/0.41 69[0:MRR:68.0,1.0] || -> . % 0.19/0.41 % SZS output end Refutation % 0.19/0.41 Formulae used in the proof : additive_inverse_not_equal_to_additive_identity_1 existence_of_identity_addition existence_of_inverse_addition well_definedness_of_additive_identity well_definedness_of_additive_inverse symmetry_of_equality transitivity_of_equality % 0.19/0.41 %------------------------------------------------------------------------------