%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD064-3 : 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 02:28:36 EDT 2022 % Result : Unsatisfiable 0.19s 0.42s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : FLD064-3 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.07/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 7 03:56:31 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.42 % 0.19/0.42 SPASS V 3.9 % 0.19/0.42 SPASS beiseite: Proof found. % 0.19/0.42 % SZS status Theorem % 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.42 SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 44 clauses. % 0.19/0.42 SPASS allocated 75651 KBytes. % 0.19/0.42 SPASS spent 0:00:00.07 on the problem. % 0.19/0.42 0:00:00.04 for the input. % 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.42 0:00:00.00 for inferences. % 0.19/0.42 0:00:00.00 for the backtracking. % 0.19/0.42 0:00:00.00 for the reduction. % 0.19/0.42 % 0.19/0.42 % 0.19/0.42 Here is a proof with depth 4, length 15 : % 0.19/0.42 % SZS output start Refutation % 0.19/0.42 1[0:Inp] || -> defined(a)*. % 0.19/0.42 2[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 0.19/0.42 3[0:Inp] || less_or_equal(additive_inverse(a),additive_identity)*l -> . % 0.19/0.42 6[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*. % 0.19/0.42 7[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*. % 0.19/0.42 8[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 0.19/0.42 18[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 0.19/0.42 27[0:Inp] || less_or_equal(u,v)* sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.19/0.42 37[0:Res:27.3,3.0] || less_or_equal(u,v)* sum__dfg(v,w,additive_identity)* sum__dfg(u,w,additive_inverse(a))* -> . % 0.19/0.42 39[0:Res:2.0,37.0] || sum__dfg(a,u,additive_identity) sum__dfg(additive_identity,u,additive_inverse(a))* -> . % 0.19/0.42 53[0:Res:7.1,8.0] defined(u) || -> sum__dfg(u,additive_inverse(u),additive_identity)*. % 0.19/0.42 59[0:Res:6.1,39.1] defined(additive_inverse(a)) || sum__dfg(a,additive_inverse(a),additive_identity)* -> . % 0.19/0.42 60[0:SSi:59.0,18.0,1.1] || sum__dfg(a,additive_inverse(a),additive_identity)* -> . % 0.19/0.42 61[0:Res:53.1,60.0] defined(a) || -> . % 0.19/0.42 62[0:SSi:61.0,1.0] || -> . % 0.19/0.42 % SZS output end Refutation % 0.19/0.42 Formulae used in the proof : a_is_defined less_or_equal_2 not_less_or_equal_3 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_additive_inverse compatibility_of_order_relation_and_addition % 0.19/0.42 %------------------------------------------------------------------------------