%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD068-4 : TPTP v8.1.0. Bugfixed v2.1.0. % 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 : Sat Jul 16 02:28:38 EDT 2022 % Result : Unsatisfiable 0.18s 0.42s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : FLD068-4 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n024.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 18:03:20 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.42 % 0.18/0.42 SPASS V 3.9 % 0.18/0.42 SPASS beiseite: Proof found. % 0.18/0.42 % SZS status Theorem % 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.18/0.42 SPASS derived 100 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses. % 0.18/0.42 SPASS allocated 75761 KBytes. % 0.18/0.42 SPASS spent 0:00:00.08 on the problem. % 0.18/0.42 0:00:00.04 for the input. % 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.42 0:00:00.00 for inferences. % 0.18/0.42 0:00:00.00 for the backtracking. % 0.18/0.42 0:00:00.01 for the reduction. % 0.18/0.42 % 0.18/0.42 % 0.18/0.42 Here is a proof with depth 5, length 21 : % 0.18/0.42 % SZS output start Refutation % 0.18/0.42 1[0:Inp] || -> defined(a)*. % 0.18/0.42 2[0:Inp] || -> defined(b)*. % 0.18/0.42 4[0:Inp] || -> sum__dfg(b,additive_inverse(a),u__dfg)*. % 0.18/0.42 5[0:Inp] || -> less_or_equal(additive_identity,u__dfg)*r. % 0.18/0.42 6[0:Inp] || less_or_equal(a,b)*l -> . % 0.18/0.42 8[0:Inp] || sum__dfg(u,v,w)*+ sum__dfg(x,y,v)* sum__dfg(u,x,z)* -> sum__dfg(z,y,w)*. % 0.18/0.42 9[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*. % 0.18/0.42 10[0:Inp] defined(u) || -> sum__dfg(additive_inverse(u),u,additive_identity)*. % 0.18/0.42 11[0:Inp] || sum__dfg(u,v,w)*+ -> sum__dfg(v,u,w)*. % 0.18/0.42 30[0:Inp] || less_or_equal(u,v)* sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.18/0.42 36[0:Res:4.0,8.0] || sum__dfg(b,u,v)* sum__dfg(additive_inverse(a),w,u)*+ -> sum__dfg(u__dfg,w,v)*. % 0.18/0.42 52[0:Res:30.3,6.0] || less_or_equal(u,v)* sum__dfg(v,w,b)* sum__dfg(u,w,a)* -> . % 0.18/0.42 62[0:Res:5.0,52.0] || sum__dfg(u__dfg,u,b)* sum__dfg(additive_identity,u,a) -> . % 0.18/0.42 80[0:Res:9.1,11.0] defined(u) || -> sum__dfg(u,additive_identity,u)*. % 0.18/0.42 116[0:Res:10.1,36.1] defined(a) || sum__dfg(b,additive_identity,u)* -> sum__dfg(u__dfg,a,u). % 0.18/0.42 122[0:SSi:116.0,1.0] || sum__dfg(b,additive_identity,u)* -> sum__dfg(u__dfg,a,u). % 0.18/0.42 130[0:Res:80.1,122.0] defined(b) || -> sum__dfg(u__dfg,a,b)*. % 0.18/0.42 132[0:SSi:130.0,2.0] || -> sum__dfg(u__dfg,a,b)*. % 0.18/0.42 151[0:Res:132.0,62.0] || sum__dfg(additive_identity,a,a)* -> . % 0.18/0.42 156[0:Res:9.1,151.0] defined(a) || -> . % 0.18/0.42 157[0:SSi:156.0,1.0] || -> . % 0.18/0.42 % SZS output end Refutation % 0.18/0.42 Formulae used in the proof : a_is_defined b_is_defined sum_4 less_or_equal_5 not_less_or_equal_6 associativity_addition_2 existence_of_identity_addition existence_of_inverse_addition commutativity_addition compatibility_of_order_relation_and_addition % 0.18/0.42 %------------------------------------------------------------------------------