%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD067-3 : 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 02:28:37 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 % 0.11/0.12 % Problem : FLD067-3 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.11/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n021.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 02:36:51 EDT 2022 % 0.12/0.33 % 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/sandbox2/benchmark/theBenchmark.p % 0.19/0.41 SPASS derived 41 clauses, backtracked 0 clauses, performed 0 splits and kept 59 clauses. % 0.19/0.41 SPASS allocated 75682 KBytes. % 0.19/0.41 SPASS spent 0:00:00.07 on the problem. % 0.19/0.41 0:00:00.03 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 0:00:00.01 for the reduction. % 0.19/0.41 % 0.19/0.41 % 0.19/0.41 Here is a proof with depth 4, length 16 : % 0.19/0.41 % SZS output start Refutation % 0.19/0.41 1[0:Inp] || -> defined(a)*. % 0.19/0.41 2[0:Inp] || -> defined(b)*. % 0.19/0.41 3[0:Inp] || -> less_or_equal(a,b)*l. % 0.19/0.41 4[0:Inp] || less_or_equal(additive_identity,add(b,additive_inverse(a)))*r -> . % 0.19/0.41 8[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*. % 0.19/0.41 9[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 0.19/0.41 19[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 0.19/0.41 23[0:Inp] defined(u) defined(v) || -> sum__dfg(v,u,add(v,u))*. % 0.19/0.41 28[0:Inp] || less_or_equal(u,v)* sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.19/0.41 37[0:Res:28.3,4.0] || less_or_equal(u,v)* sum__dfg(u,w,additive_identity)* sum__dfg(v,w,add(b,additive_inverse(a)))* -> . % 0.19/0.41 39[0:Res:3.0,37.0] || sum__dfg(a,u,additive_identity) sum__dfg(b,u,add(b,additive_inverse(a)))* -> . % 0.19/0.41 52[0:Res:8.1,9.0] defined(u) || -> sum__dfg(u,additive_inverse(u),additive_identity)*. % 0.19/0.41 79[0:Res:23.2,39.1] defined(additive_inverse(a)) defined(b) || sum__dfg(a,additive_inverse(a),additive_identity)* -> . % 0.19/0.41 80[0:SSi:79.1,79.0,2.0,19.1,1.0] || sum__dfg(a,additive_inverse(a),additive_identity)* -> . % 0.19/0.41 81[0:Res:52.1,80.0] defined(a) || -> . % 0.19/0.41 82[0:SSi:81.0,1.0] || -> . % 0.19/0.41 % SZS output end Refutation % 0.19/0.41 Formulae used in the proof : a_is_defined b_is_defined less_or_equal_3 not_less_or_equal_4 existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse totality_of_addition compatibility_of_order_relation_and_addition % 0.19/0.41 %------------------------------------------------------------------------------