%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n024.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 : Wed Jul 20 21:41:00 EDT 2022 % Result : Unsatisfiable 0.20s 0.42s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV019-1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.13 % Command : run_spass %d %s % 0.14/0.34 % Computer : n024.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Tue Jun 14 22:27:48 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.42 % 0.20/0.42 SPASS V 3.9 % 0.20/0.42 SPASS beiseite: Proof found. % 0.20/0.42 % SZS status Theorem % 0.20/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 SPASS derived 121 clauses, backtracked 0 clauses, performed 0 splits and kept 60 clauses. % 0.20/0.42 SPASS allocated 63181 KBytes. % 0.20/0.42 SPASS spent 0:00:00.06 on the problem. % 0.20/0.42 0:00:00.03 for the input. % 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.20/0.42 0:00:00.00 for inferences. % 0.20/0.42 0:00:00.00 for the backtracking. % 0.20/0.42 0:00:00.01 for the reduction. % 0.20/0.42 % 0.20/0.42 % 0.20/0.42 Here is a proof with depth 5, length 25 : % 0.20/0.42 % SZS output start Refutation % 0.20/0.42 1[0:Inp] || -> less_than(u,lower_bound) in_array_bounds(array,u)* less_than(upper_bound,u). % 0.20/0.42 2[0:Inp] || less_than(successor(u),successor(v))* -> less_than(u,v). % 0.20/0.42 3[0:Inp] || less_than(u,v)* less_than(v,w)* -> less_than(u,w)*. % 0.20/0.42 4[0:Inp] || -> less_than(u,successor(u))*r. % 0.20/0.42 5[0:Inp] || in_array_bounds(array,index_of_maximal) -> equal(array_value_at(array,index_of_maximal),maximal_value)**. % 0.20/0.42 6[0:Inp] || -> less_than(index_of_maximal,an_index)*r. % 0.20/0.42 7[0:Inp] || less_than(an_index,lower_bound)*l -> . % 0.20/0.42 8[0:Inp] || less_than(upper_bound,an_index)*r -> . % 0.20/0.42 9[0:Inp] || less_than(index_of_maximal,lower_bound)*l -> . % 0.20/0.42 10[0:Inp] || in_array_bounds(array,an_index) less_than(index_of_maximal,successor(an_index)) in_array_bounds(array,index_of_maximal) equal(array_value_at(array,index_of_maximal),maximal_value)** -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)) less_than(index_of_maximal,lower_bound). % 0.20/0.42 11[0:Rew:5.1,10.3] || in_array_bounds(array,an_index)* less_than(index_of_maximal,successor(an_index)) in_array_bounds(array,index_of_maximal) equal(maximal_value,maximal_value) -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)) less_than(index_of_maximal,lower_bound). % 0.20/0.42 12[0:Obv:11.3] || in_array_bounds(array,an_index)* less_than(index_of_maximal,successor(an_index)) in_array_bounds(array,index_of_maximal) -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)) less_than(index_of_maximal,lower_bound). % 0.20/0.42 13[0:MRR:12.5,9.0] || in_array_bounds(array,index_of_maximal) in_array_bounds(array,an_index)* less_than(index_of_maximal,successor(an_index)) -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 14[0:NCh:3.2,3.1,8.0,6.0] || less_than(upper_bound,index_of_maximal)*r -> . % 0.20/0.42 18[0:NCh:3.2,3.1,2.0,4.0] || less_than(successor(u),v)* -> less_than(u,v). % 0.20/0.42 36[0:Res:1.1,13.1] || in_array_bounds(array,index_of_maximal)* less_than(index_of_maximal,successor(an_index)) -> less_than(an_index,lower_bound) less_than(upper_bound,an_index) less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 37[0:MRR:36.2,36.3,7.0,8.0] || in_array_bounds(array,index_of_maximal)* less_than(index_of_maximal,successor(an_index)) -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 57[0:Res:1.1,37.0] || less_than(index_of_maximal,successor(an_index))*r -> less_than(index_of_maximal,lower_bound) less_than(upper_bound,index_of_maximal) less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 58[0:MRR:57.1,57.2,9.0,14.0] || less_than(index_of_maximal,successor(an_index))*r -> less_than(successor(an_index),lower_bound) less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 117[0:NCh:3.2,3.1,58.0,4.0] || less_than(index_of_maximal,an_index) -> less_than(successor(an_index),lower_bound)*l less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 119[0:MRR:117.0,6.0] || -> less_than(successor(an_index),lower_bound)*l less_than(successor(upper_bound),successor(an_index)). % 0.20/0.42 121[0:Res:119.0,18.0] || -> less_than(successor(upper_bound),successor(an_index))*r less_than(an_index,lower_bound). % 0.20/0.42 129[0:MRR:121.1,7.0] || -> less_than(successor(upper_bound),successor(an_index))*r. % 0.20/0.42 130[0:Res:129.0,2.0] || -> less_than(upper_bound,an_index)*r. % 0.20/0.42 139[0:MRR:130.0,8.0] || -> . % 0.20/0.42 % SZS output end Refutation % 0.20/0.42 Formulae used in the proof : in_bounds predecessor_less transitivity_of_less successor_greater this_is_maximal maximal_before_somewhere somewhere_above_lower_bound somewhere_below_upper_bound maximal_above_lower_bound prove_this % 0.20/0.42 %------------------------------------------------------------------------------