%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD058-3 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n027.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 02:28:34 EDT 2022 % Result : Unsatisfiable 0.76s 0.97s % Output : Refutation 0.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : FLD058-3 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.07/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n027.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 14:48:09 EDT 2022 % 0.12/0.33 % CPUTime : % 0.76/0.97 % 0.76/0.97 SPASS V 3.9 % 0.76/0.97 SPASS beiseite: Proof found. % 0.76/0.97 % SZS status Theorem % 0.76/0.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.76/0.97 SPASS derived 2794 clauses, backtracked 0 clauses, performed 0 splits and kept 1557 clauses. % 0.76/0.97 SPASS allocated 77648 KBytes. % 0.76/0.97 SPASS spent 0:00:00.62 on the problem. % 0.76/0.97 0:00:00.04 for the input. % 0.76/0.97 0:00:00.00 for the FLOTTER CNF translation. % 0.76/0.97 0:00:00.02 for inferences. % 0.76/0.97 0:00:00.00 for the backtracking. % 0.76/0.97 0:00:00.53 for the reduction. % 0.76/0.97 % 0.76/0.97 % 0.76/0.97 Here is a proof with depth 6, length 35 : % 0.76/0.97 % SZS output start Refutation % 0.76/0.97 2[0:Inp] || -> defined(b)*. % 0.76/0.97 3[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 0.76/0.97 4[0:Inp] || -> less_or_equal(a,b)*l. % 0.76/0.97 5[0:Inp] || sum__dfg(additive_identity,a,additive_identity)* -> . % 0.76/0.97 6[0:Inp] || -> sum__dfg(additive_identity,b,additive_identity)*. % 0.76/0.97 8[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*. % 0.76/0.97 9[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*. % 0.76/0.97 11[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 0.76/0.97 27[0:Inp] || less_or_equal(u,v) less_or_equal(v,u) -> sum__dfg(additive_identity,v,u)*. % 0.76/0.97 28[0:Inp] || less_or_equal(u,v)* less_or_equal(v,w)* -> less_or_equal(u,w)*. % 0.76/0.97 30[0:Inp] || less_or_equal(u,v)*+ sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.76/0.97 36[0:Res:6.0,8.0] || sum__dfg(additive_identity,u,v)*+ sum__dfg(b,w,u)* -> sum__dfg(additive_identity,w,v)*. % 0.76/0.97 37[0:Res:6.0,11.0] || -> sum__dfg(b,additive_identity,additive_identity)*. % 0.76/0.97 39[0:Res:6.0,30.1] || less_or_equal(additive_identity,u) sum__dfg(u,b,v)* -> less_or_equal(additive_identity,v). % 0.76/0.97 41[0:Res:6.0,8.1] || sum__dfg(u,additive_identity,v)*+ sum__dfg(u,additive_identity,w)* -> sum__dfg(w,b,v)*. % 0.76/0.97 43[0:Res:6.0,30.2] || less_or_equal(u,additive_identity) sum__dfg(u,b,v)* -> less_or_equal(v,additive_identity). % 0.76/0.97 58[0:Res:3.0,27.1] || less_or_equal(a,additive_identity) -> sum__dfg(additive_identity,a,additive_identity)*. % 0.76/0.97 62[0:MRR:58.1,5.0] || less_or_equal(a,additive_identity)*l -> . % 0.76/0.97 89[0:OCh:28.1,28.0,3.0,4.0] || -> less_or_equal(additive_identity,b)*r. % 0.76/0.97 90[0:NCh:28.2,28.0,62.0,4.0] || less_or_equal(b,additive_identity)*l -> . % 0.76/0.97 98[0:Res:9.1,11.0] defined(u) || -> sum__dfg(u,additive_identity,u)*. % 0.76/0.97 169[0:Res:9.1,36.0] defined(u) || sum__dfg(b,v,u)* -> sum__dfg(additive_identity,v,u). % 0.76/0.97 266[0:Res:98.1,169.1] defined(b) defined(b) || -> sum__dfg(additive_identity,additive_identity,b)*. % 0.76/0.97 270[0:Obv:266.0] defined(b) || -> sum__dfg(additive_identity,additive_identity,b)*. % 0.76/0.97 271[0:SSi:270.0,2.0] || -> sum__dfg(additive_identity,additive_identity,b)*. % 0.76/0.97 289[0:Res:271.0,36.0] || sum__dfg(b,u,additive_identity)* -> sum__dfg(additive_identity,u,b). % 0.76/0.97 493[0:Res:37.0,41.0] || sum__dfg(b,additive_identity,u)*+ -> sum__dfg(u,b,additive_identity)*. % 0.76/0.97 609[0:Res:98.1,493.0] defined(b) || -> sum__dfg(b,b,additive_identity)*. % 0.76/0.97 617[0:SSi:609.0,2.0] || -> sum__dfg(b,b,additive_identity)*. % 0.76/0.97 627[0:Res:617.0,289.0] || -> sum__dfg(additive_identity,b,b)*. % 0.76/0.97 3058[0:Res:617.0,39.1] || less_or_equal(additive_identity,b)*r -> less_or_equal(additive_identity,additive_identity). % 0.76/0.97 3098[0:MRR:3058.0,89.0] || -> less_or_equal(additive_identity,additive_identity)*. % 0.76/0.97 3201[0:Res:627.0,43.1] || less_or_equal(additive_identity,additive_identity) -> less_or_equal(b,additive_identity)*l. % 0.76/0.97 3228[0:MRR:3201.1,90.0] || less_or_equal(additive_identity,additive_identity)* -> . % 0.76/0.97 3229[0:MRR:3228.0,3098.0] || -> . % 0.76/0.97 % SZS output end Refutation % 0.76/0.97 Formulae used in the proof : b_is_defined less_or_equal_3 less_or_equal_4 not_sum_5 sum_6 associativity_addition_2 existence_of_identity_addition commutativity_addition antisymmetry_of_order_relation transitivity_of_order_relation compatibility_of_order_relation_and_addition % 0.76/0.97 %------------------------------------------------------------------------------