%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD013-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n023.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 02:28:16 EDT 2022 % Result : Unsatisfiable 0.20s 0.46s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : FLD013-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.12/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n023.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 : Mon Jun 6 11:56:24 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.46 % 0.20/0.46 SPASS V 3.9 % 0.20/0.46 SPASS beiseite: Proof found. % 0.20/0.46 % SZS status Theorem % 0.20/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.20/0.46 SPASS derived 230 clauses, backtracked 0 clauses, performed 0 splits and kept 185 clauses. % 0.20/0.46 SPASS allocated 75939 KBytes. % 0.20/0.46 SPASS spent 0:00:00.10 on the problem. % 0.20/0.46 0:00:00.04 for the input. % 0.20/0.46 0:00:00.00 for the FLOTTER CNF translation. % 0.20/0.46 0:00:00.01 for inferences. % 0.20/0.46 0:00:00.00 for the backtracking. % 0.20/0.46 0:00:00.03 for the reduction. % 0.20/0.46 % 0.20/0.46 % 0.20/0.46 Here is a proof with depth 4, length 21 : % 0.20/0.46 % SZS output start Refutation % 0.20/0.46 2[0:Inp] || -> defined(b)*. % 0.20/0.46 3[0:Inp] || -> defined(c)*. % 0.20/0.46 6[0:Inp] || -> equalish(a,b)*l. % 0.20/0.46 7[0:Inp] || -> equalish(c,d)*l. % 0.20/0.46 8[0:Inp] || -> equalish(add(a,c),u__dfg)*l. % 0.20/0.46 9[0:Inp] || equalish(add(d,b),u__dfg)*l -> . % 0.20/0.46 13[0:Inp] defined(u) defined(v) || -> equalish(add(v,u),add(u,v))*. % 0.20/0.46 31[0:Inp] || equalish(u,v)* -> equalish(v,u). % 0.20/0.46 32[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.20/0.46 33[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*. % 0.20/0.46 39[0:Res:7.0,33.1] defined(u) || -> equalish(add(c,u),add(d,u))*l. % 0.20/0.46 43[0:Res:6.0,33.1] defined(u) || -> equalish(add(a,u),add(b,u))*l. % 0.20/0.46 45[0:Res:8.0,31.0] || -> equalish(u__dfg,add(a,c))*r. % 0.20/0.46 49[0:Res:31.1,9.0] || equalish(u__dfg,add(d,b))*r -> . % 0.20/0.46 65[0:OCh:32.1,32.0,43.1,45.0] defined(c) || -> equalish(u__dfg,add(b,c))*r. % 0.20/0.46 66[0:SSi:65.0,3.0] || -> equalish(u__dfg,add(b,c))*r. % 0.20/0.46 142[0:OCh:32.1,32.0,13.2,66.0] defined(c) defined(b) || -> equalish(u__dfg,add(c,b))*r. % 0.20/0.46 152[0:SSi:142.1,142.0,2.0,3.0] || -> equalish(u__dfg,add(c,b))*r. % 0.20/0.46 372[0:OCh:32.1,32.0,39.1,152.0] defined(b) || -> equalish(u__dfg,add(d,b))*r. % 0.20/0.46 376[0:SSi:372.0,2.0] || -> equalish(u__dfg,add(d,b))*r. % 0.20/0.46 377[0:MRR:376.0,49.0] || -> . % 0.20/0.46 % SZS output end Refutation % 0.20/0.46 Formulae used in the proof : b_is_defined c_is_defined a_equals_b_6 c_equals_d_7 add_equals_u_8 add_not_equal_to_u_9 commutativity_addition symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition % 0.20/0.46 %------------------------------------------------------------------------------