%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD018-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n026.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 02:28:18 EDT 2022 % Result : Unsatisfiable 0.18s 0.42s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : FLD018-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.11/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n026.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 23:13:16 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.42 % 0.18/0.42 SPASS V 3.9 % 0.18/0.42 SPASS beiseite: Proof found. % 0.18/0.42 % SZS status Theorem % 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.18/0.42 SPASS derived 121 clauses, backtracked 0 clauses, performed 0 splits and kept 94 clauses. % 0.18/0.42 SPASS allocated 75771 KBytes. % 0.18/0.42 SPASS spent 0:00:00.07 on the problem. % 0.18/0.42 0:00:00.03 for the input. % 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.42 0:00:00.00 for inferences. % 0.18/0.42 0:00:00.00 for the backtracking. % 0.18/0.42 0:00:00.01 for the reduction. % 0.18/0.42 % 0.18/0.42 % 0.18/0.42 Here is a proof with depth 3, length 17 : % 0.18/0.42 % SZS output start Refutation % 0.18/0.42 1[0:Inp] || -> defined(a)*. % 0.18/0.42 2[0:Inp] || -> equalish(a,additive_identity)*l. % 0.18/0.42 3[0:Inp] || equalish(additive_inverse(a),additive_identity)*l -> . % 0.18/0.42 5[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 0.18/0.42 6[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 0.18/0.42 15[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 0.18/0.42 25[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.18/0.42 26[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.18/0.42 27[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*. % 0.18/0.42 33[0:Res:2.0,27.1] defined(u) || -> equalish(add(a,u),add(additive_identity,u))*l. % 0.18/0.42 37[0:Res:25.1,3.0] || equalish(additive_identity,additive_inverse(a))*r -> . % 0.18/0.42 48[0:Res:6.1,25.0] defined(u) || -> equalish(additive_identity,add(u,additive_inverse(u)))*r. % 0.18/0.42 177[0:OCh:26.1,26.0,48.1,33.1] defined(a) defined(additive_inverse(a)) || -> equalish(additive_identity,add(additive_identity,additive_inverse(a)))*r. % 0.18/0.42 180[0:SSi:177.1,177.0,15.0,1.0,1.1] || -> equalish(additive_identity,add(additive_identity,additive_inverse(a)))*r. % 0.18/0.42 204[0:OCh:26.1,26.0,180.0,5.1] defined(additive_inverse(a)) || -> equalish(additive_identity,additive_inverse(a))*r. % 0.18/0.42 206[0:SSi:204.0,15.0,1.1] || -> equalish(additive_identity,additive_inverse(a))*r. % 0.18/0.42 207[0:MRR:206.0,37.0] || -> . % 0.18/0.42 % SZS output end Refutation % 0.18/0.42 Formulae used in the proof : a_is_defined a_equals_additive_identity_2 additive_inverse_not_equal_to_additive_identity_3 existence_of_identity_addition existence_of_inverse_addition well_definedness_of_additive_inverse symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition % 0.18/0.42 %------------------------------------------------------------------------------