%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD030-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n018.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 02:28:23 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 % 0.07/0.11 % Problem : FLD030-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.07/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n018.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 : Tue Jun 7 02:27:05 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 137 clauses, backtracked 0 clauses, performed 0 splits and kept 109 clauses. % 0.18/0.42 SPASS allocated 75807 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 0:00:00.02 for the reduction. % 0.18/0.42 % 0.18/0.42 % 0.18/0.42 Here is a proof with depth 2, length 13 : % 0.18/0.42 % SZS output start Refutation % 0.18/0.42 2[0:Inp] || -> defined(b)*. % 0.18/0.42 5[0:Inp] || -> equalish(multiply(a,b),c)*l. % 0.18/0.42 6[0:Inp] || -> equalish(a,d)*l. % 0.18/0.42 7[0:Inp] || equalish(multiply(d,b),c)*l -> . % 0.18/0.42 29[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.18/0.42 30[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.18/0.42 32[0:Inp] defined(u) || equalish(v,w) -> equalish(multiply(v,u),multiply(w,u))*. % 0.18/0.42 36[0:Res:6.0,32.1] defined(u) || -> equalish(multiply(a,u),multiply(d,u))*l. % 0.18/0.42 39[0:Res:5.0,29.0] || -> equalish(c,multiply(a,b))*r. % 0.18/0.42 43[0:Res:29.1,7.0] || equalish(c,multiply(d,b))*r -> . % 0.18/0.42 227[0:OCh:30.1,30.0,36.1,39.0] defined(b) || -> equalish(c,multiply(d,b))*r. % 0.18/0.42 230[0:SSi:227.0,2.0] || -> equalish(c,multiply(d,b))*r. % 0.18/0.42 231[0:MRR:230.0,43.0] || -> . % 0.18/0.42 % SZS output end Refutation % 0.18/0.42 Formulae used in the proof : b_is_defined multiply_equals_c_5 a_equals_d_6 multiply_not_equal_to_c_7 symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_multiplication % 0.18/0.42 %------------------------------------------------------------------------------