%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD067-4 : 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 02:28:37 EDT 2022 % Result : Unsatisfiable 0.18s 0.41s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : FLD067-4 : 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 : Tue Jun 7 02:52:16 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.41 % 0.18/0.41 SPASS V 3.9 % 0.18/0.41 SPASS beiseite: Proof found. % 0.18/0.41 % SZS status Theorem % 0.18/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.18/0.41 SPASS derived 43 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses. % 0.18/0.41 SPASS allocated 75676 KBytes. % 0.18/0.41 SPASS spent 0:00:00.07 on the problem. % 0.18/0.41 0:00:00.04 for the input. % 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.41 0:00:00.00 for inferences. % 0.18/0.41 0:00:00.00 for the backtracking. % 0.18/0.41 0:00:00.00 for the reduction. % 0.18/0.41 % 0.18/0.41 % 0.18/0.41 Here is a proof with depth 3, length 13 : % 0.18/0.41 % SZS output start Refutation % 0.18/0.41 1[0:Inp] || -> defined(a)*. % 0.18/0.41 4[0:Inp] || -> less_or_equal(a,b)*l. % 0.18/0.41 5[0:Inp] || -> sum__dfg(b,additive_inverse(a),u__dfg)*. % 0.18/0.41 6[0:Inp] || less_or_equal(additive_identity,u__dfg)*r -> . % 0.18/0.41 10[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*. % 0.18/0.41 11[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 0.18/0.41 30[0:Inp] || less_or_equal(u,v)* sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.18/0.41 51[0:Res:30.3,6.0] || less_or_equal(u,v)* sum__dfg(v,w,u__dfg)* sum__dfg(u,w,additive_identity)* -> . % 0.18/0.41 64[0:Res:4.0,51.0] || sum__dfg(b,u,u__dfg) sum__dfg(a,u,additive_identity)* -> . % 0.18/0.41 82[0:Res:10.1,11.0] defined(u) || -> sum__dfg(u,additive_inverse(u),additive_identity)*. % 0.18/0.41 86[0:Res:82.1,64.1] defined(a) || sum__dfg(b,additive_inverse(a),u__dfg)* -> . % 0.18/0.41 87[0:SSi:86.0,1.0] || sum__dfg(b,additive_inverse(a),u__dfg)* -> . % 0.18/0.41 88[0:MRR:87.0,5.0] || -> . % 0.18/0.41 % SZS output end Refutation % 0.18/0.41 Formulae used in the proof : a_is_defined less_or_equal_4 sum_5 not_less_or_equal_6 existence_of_inverse_addition commutativity_addition compatibility_of_order_relation_and_addition % 0.18/0.41 %------------------------------------------------------------------------------