%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD067-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n018.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 02:28:37 EDT 2022 % Result : Unsatisfiable 0.19s 0.54s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : FLD067-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.00/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n018.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 : Tue Jun 7 02:21:35 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.54 % 0.19/0.54 SPASS V 3.9 % 0.19/0.54 SPASS beiseite: Proof found. % 0.19/0.54 % SZS status Theorem % 0.19/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.54 SPASS derived 628 clauses, backtracked 0 clauses, performed 1 splits and kept 404 clauses. % 0.19/0.54 SPASS allocated 76330 KBytes. % 0.19/0.54 SPASS spent 0:00:00.19 on the problem. % 0.19/0.54 0:00:00.04 for the input. % 0.19/0.54 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.54 0:00:00.01 for inferences. % 0.19/0.54 0:00:00.00 for the backtracking. % 0.19/0.54 0:00:00.12 for the reduction. % 0.19/0.54 % 0.19/0.54 % 0.19/0.54 Here is a proof with depth 5, length 24 : % 0.19/0.54 % SZS output start Refutation % 0.19/0.54 1[0:Inp] || -> defined(a)*. % 0.19/0.54 3[0:Inp] || -> less_or_equal(a,b)*l. % 0.19/0.54 4[0:Inp] || less_or_equal(additive_identity,add(b,additive_inverse(a)))*r -> . % 0.19/0.54 6[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 0.19/0.54 7[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 0.19/0.54 15[0:Inp] || -> defined(additive_identity)*. % 0.19/0.54 16[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 0.19/0.54 23[0:Inp] defined(u) || less_or_equal(v,w) -> less_or_equal(add(v,u),add(w,u))*. % 0.19/0.54 26[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.19/0.54 27[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.19/0.54 30[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 0.19/0.54 35[0:Res:3.0,23.1] defined(u) || -> less_or_equal(add(a,u),add(b,u))*l. % 0.19/0.54 37[0:Res:30.2,4.0] || equalish(u,additive_identity)* less_or_equal(u,add(b,additive_inverse(a)))*+ -> . % 0.19/0.54 52[0:Res:6.1,26.0] defined(u) || -> equalish(u,add(additive_identity,u))*r. % 0.19/0.54 53[0:Res:7.1,26.0] defined(u) || -> equalish(additive_identity,add(u,additive_inverse(u)))*r. % 0.19/0.54 63[0:OCh:27.1,27.0,52.1,7.1] defined(additive_inverse(additive_identity)) defined(additive_identity) || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 0.19/0.54 66[0:SSi:63.1,63.0,15.0,16.1,15.0] || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 0.19/0.54 68[0:NCh:27.2,27.0,66.0,26.0] || equalish(additive_identity,u)*+ -> equalish(u,additive_inverse(additive_identity))*. % 0.19/0.54 228[0:Res:53.1,68.0] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_inverse(additive_identity))*l. % 0.19/0.54 787[0:Res:35.1,37.1] defined(additive_inverse(a)) || equalish(add(a,additive_inverse(a)),additive_identity)*l -> . % 0.19/0.54 803[0:SSi:787.0,16.0,1.1] || equalish(add(a,additive_inverse(a)),additive_identity)*l -> . % 0.19/0.54 812[0:NCh:27.2,27.0,803.0,228.1] defined(a) || equalish(additive_inverse(additive_identity),additive_identity)*l -> . % 0.19/0.54 816[0:SSi:812.0,1.0] || equalish(additive_inverse(additive_identity),additive_identity)*l -> . % 0.19/0.54 817[0:MRR:816.0,66.0] || -> . % 0.19/0.54 % SZS output end Refutation % 0.19/0.54 Formulae used in the proof : a_is_defined less_or_equal_3 not_less_or_equal_4 existence_of_identity_addition existence_of_inverse_addition well_definedness_of_additive_identity well_definedness_of_additive_inverse compatibility_of_order_relation_and_addition symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_order_relation % 0.19/0.54 %------------------------------------------------------------------------------