%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n016.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 : Mon Jul 18 14:23:45 EDT 2022 % Result : Unsatisfiable 0.19s 0.49s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0. % 0.06/0.13 % Command : run_spass %d %s % 0.12/0.33 % Computer : n016.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 : Wed Jul 6 14:10:35 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.49 % 0.19/0.49 SPASS V 3.9 % 0.19/0.49 SPASS beiseite: Proof found. % 0.19/0.49 % SZS status Theorem % 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.49 SPASS derived 667 clauses, backtracked 0 clauses, performed 0 splits and kept 415 clauses. % 0.19/0.49 SPASS allocated 63658 KBytes. % 0.19/0.49 SPASS spent 0:00:00.14 on the problem. % 0.19/0.49 0:00:00.04 for the input. % 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.49 0:00:00.02 for inferences. % 0.19/0.49 0:00:00.00 for the backtracking. % 0.19/0.49 0:00:00.06 for the reduction. % 0.19/0.49 % 0.19/0.49 % 0.19/0.49 Here is a proof with depth 2, length 17 : % 0.19/0.49 % SZS output start Refutation % 0.19/0.49 4[0:Inp] || equalish(u,v) -> equalish(multiply(u,w),multiply(v,w))*. % 0.19/0.49 5[0:Inp] || equalish(u,v) less(u,v)* -> . % 0.19/0.49 6[0:Inp] || -> less(u,v)* equalish(u,v) less(v,u)*. % 0.19/0.49 7[0:Inp] || less(u,u)* -> . % 0.19/0.49 9[0:Inp] || less(u,v) -> equalish(w,n0) less(multiply(u,w),multiply(v,w))*. % 0.19/0.49 10[0:Inp] || less(b,a)*l -> . % 0.19/0.49 11[0:Inp] || -> less(multiply(b,c),multiply(a,c))*l. % 0.19/0.49 12[0:Inp] || equalish(c,n0)*r -> . % 0.19/0.49 19[0:Inp] || less(u,v)* less(v,w)* -> less(u,w)*. % 0.19/0.49 51[0:Res:11.0,5.1] || equalish(multiply(b,c),multiply(a,c))*l -> . % 0.19/0.49 188[0:Res:4.1,51.0] || equalish(b,a)*l -> . % 0.19/0.49 255[0:Res:6.0,10.0] || -> equalish(b,a) less(a,b)*r. % 0.19/0.49 300[0:MRR:255.0,188.0] || -> less(a,b)*r. % 0.19/0.49 333[0:OCh:19.1,19.0,9.2,11.0] || less(u,b) -> equalish(c,n0) less(multiply(u,c),multiply(a,c))*. % 0.19/0.49 339[0:MRR:333.1,12.0] || less(u,b) -> less(multiply(u,c),multiply(a,c))*. % 0.19/0.49 686[0:Res:339.1,7.0] || less(a,b)*r -> . % 0.19/0.49 700[0:MRR:686.0,300.0] || -> . % 0.19/0.49 % SZS output end Refutation % 0.19/0.49 Formulae used in the proof : equality_preserved_over_times not_less_and_equal numbers_either_less_or_equal number_not_less_than_itself multiply_lemma b_not_less_than_a b_times_c_less_than_a_times_c prove_c_is_0 transitivity_of_less % 0.19/0.49 %------------------------------------------------------------------------------