%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM004-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n014.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 14:23:36 EDT 2022 % Result : Unsatisfiable 0.17s 0.54s % Output : Refutation 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : NUM004-1 : TPTP v8.1.0. Released v1.0.0. % 0.10/0.12 % Command : run_spass %d %s % 0.11/0.32 % Computer : n014.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Tue Jul 5 22:36:38 EDT 2022 % 0.11/0.32 % CPUTime : % 0.17/0.54 % 0.17/0.54 SPASS V 3.9 % 0.17/0.54 SPASS beiseite: Proof found. % 0.17/0.54 % SZS status Theorem % 0.17/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.17/0.54 SPASS derived 638 clauses, backtracked 0 clauses, performed 0 splits and kept 393 clauses. % 0.17/0.54 SPASS allocated 64033 KBytes. % 0.17/0.54 SPASS spent 0:00:00.20 on the problem. % 0.17/0.54 0:00:00.04 for the input. % 0.17/0.54 0:00:00.00 for the FLOTTER CNF translation. % 0.17/0.54 0:00:00.02 for inferences. % 0.17/0.54 0:00:00.00 for the backtracking. % 0.17/0.54 0:00:00.12 for the reduction. % 0.17/0.54 % 0.17/0.54 % 0.17/0.54 Here is a proof with depth 3, length 11 : % 0.17/0.54 % SZS output start Refutation % 0.17/0.54 1[0:Inp] || equalish(subtract(add(a,b),c),add(a,subtract(b,c)))*r -> . % 0.17/0.54 2[0:Inp] || -> equalish(u,u)*. % 0.17/0.54 3[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.17/0.54 4[0:Inp] || -> equalish(add(u,v),add(v,u))*. % 0.17/0.54 9[0:Inp] || -> equalish(subtract(add(u,v),w),add(subtract(u,w),v))*r. % 0.17/0.54 12[0:Inp] || equalish(u,v)* equalish(w,subtract(u,x))*+ -> equalish(w,subtract(v,x))*. % 0.17/0.54 19[0:OCh:3.1,3.0,9.0,4.0] || -> equalish(subtract(add(u,v),w),add(v,subtract(u,w)))*r. % 0.17/0.54 29[0:NCh:3.2,3.1,1.0,19.0] || equalish(subtract(add(a,b),c),subtract(add(b,a),c))*l -> . % 0.17/0.54 89[0:Res:2.0,12.1] || equalish(u,v) -> equalish(subtract(u,w),subtract(v,w))*. % 0.17/0.54 632[0:Res:89.1,29.0] || equalish(add(a,b),add(b,a))*l -> . % 0.17/0.54 652[0:MRR:632.0,4.0] || -> . % 0.17/0.54 % SZS output end Refutation % 0.17/0.54 Formulae used in the proof : prove_equation reflexivity transitivity commutativity_of_addition commutativity2 subtract_substitution1 % 0.17/0.54 %------------------------------------------------------------------------------