%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM001-1 : TPTP v8.1.0. Released v1.0.0. % 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 14:23:35 EDT 2022 % Result : Unsatisfiable 0.19s 0.41s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM001-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.13 % Command : run_spass %d %s % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % 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 : Wed Jul 6 03:45:49 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.41 % 0.19/0.41 SPASS V 3.9 % 0.19/0.41 SPASS beiseite: Proof found. % 0.19/0.41 % SZS status Theorem % 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.41 SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 25 clauses. % 0.19/0.41 SPASS allocated 63141 KBytes. % 0.19/0.41 SPASS spent 0:00:00.06 on the problem. % 0.19/0.41 0:00:00.04 for the input. % 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.41 0:00:00.00 for inferences. % 0.19/0.41 0:00:00.00 for the backtracking. % 0.19/0.41 0:00:00.00 for the reduction. % 0.19/0.41 % 0.19/0.41 % 0.19/0.41 Here is a proof with depth 2, length 8 : % 0.19/0.41 % SZS output start Refutation % 0.19/0.41 1[0:Inp] || equalish(add(add(a,b),c),add(a,add(b,c)))*l -> . % 0.19/0.41 3[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.19/0.41 4[0:Inp] || -> equalish(add(u,v),add(v,u))*. % 0.19/0.41 5[0:Inp] || -> equalish(add(u,add(v,w)),add(add(u,v),w))*r. % 0.19/0.41 22[0:OCh:3.1,3.0,5.0,4.0] || -> equalish(add(u,add(v,w)),add(w,add(u,v)))*. % 0.19/0.41 29[0:NCh:3.2,3.0,1.0,4.0] || equalish(add(c,add(a,b)),add(a,add(b,c)))*r -> . % 0.19/0.41 32[0:OCh:3.1,3.0,22.0,22.0] || -> equalish(add(u,add(v,w)),add(v,add(w,u)))*. % 0.19/0.41 37[0:UnC:32.0,29.0] || -> . % 0.19/0.41 % SZS output end Refutation % 0.19/0.41 Formulae used in the proof : prove_equation transitivity commutativity_of_addition associativity_of_addition % 0.19/0.41 %------------------------------------------------------------------------------