%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM002-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n008.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 1.58s 1.81s % Output : Refutation 1.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM002-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n008.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 09:22:23 EDT 2022 % 0.12/0.34 % CPUTime : % 1.58/1.81 % 1.58/1.81 SPASS V 3.9 % 1.58/1.81 SPASS beiseite: Proof found. % 1.58/1.81 % SZS status Theorem % 1.58/1.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.58/1.81 SPASS derived 2780 clauses, backtracked 0 clauses, performed 0 splits and kept 1829 clauses. % 1.58/1.81 SPASS allocated 67410 KBytes. % 1.58/1.81 SPASS spent 0:00:01.43 on the problem. % 1.58/1.81 0:00:00.03 for the input. % 1.58/1.81 0:00:00.00 for the FLOTTER CNF translation. % 1.58/1.81 0:00:00.05 for inferences. % 1.58/1.81 0:00:00.00 for the backtracking. % 1.58/1.81 0:00:01.32 for the reduction. % 1.58/1.81 % 1.58/1.81 % 1.58/1.81 Here is a proof with depth 6, length 21 : % 1.58/1.81 % SZS output start Refutation % 1.58/1.81 1[0:Inp] || equalish(add(subtract(a,b),c),add(a,subtract(c,b)))*l -> . % 1.58/1.81 3[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 1.58/1.81 4[0:Inp] || -> equalish(add(u,v),add(v,u))*. % 1.58/1.81 5[0:Inp] || -> equalish(add(u,add(v,w)),add(add(u,v),w))*r. % 1.58/1.81 6[0:Inp] || -> equalish(subtract(add(u,v),v),u)*l. % 1.58/1.81 7[0:Inp] || -> equalish(u,subtract(add(u,v),v))*r. % 1.58/1.81 8[0:Inp] || -> equalish(add(subtract(u,v),w),subtract(add(u,w),v))*r. % 1.58/1.81 9[0:Inp] || -> equalish(subtract(add(u,v),w),add(subtract(u,w),v))*l. % 1.58/1.81 10[0:Inp] || equalish(u,v)* equalish(w,add(u,x))*+ -> equalish(w,add(v,x))*. % 1.58/1.81 12[0:Inp] || equalish(u,v)* equalish(w,subtract(u,x))*+ -> equalish(w,subtract(v,x))*. % 1.58/1.81 14[0:Res:10.2,1.0] || equalish(u,a) equalish(add(subtract(a,b),c),add(u,subtract(c,b)))* -> . % 1.58/1.81 21[0:OCh:3.1,3.0,8.0,6.0] || -> equalish(add(subtract(u,v),v),u)*l. % 1.58/1.81 23[0:OCh:3.1,3.0,21.0,4.0] || -> equalish(add(u,subtract(v,u)),v)*l. % 1.58/1.81 25[0:OCh:3.1,3.0,5.0,4.0] || -> equalish(add(u,add(v,w)),add(w,add(u,v)))*. % 1.58/1.81 28[0:OCh:3.1,3.0,25.0,4.0] || -> equalish(add(add(u,v),w),add(v,add(w,u)))*l. % 1.58/1.81 116[0:Res:7.0,12.1] || equalish(add(u,v),w)*+ -> equalish(u,subtract(w,v))*. % 1.58/1.81 609[0:Res:28.0,116.0] || -> equalish(add(u,v),subtract(add(v,add(w,u)),w))*r. % 1.58/1.81 842[0:OCh:3.1,3.0,609.0,9.0] || -> equalish(add(u,v),add(subtract(v,w),add(w,u)))*r. % 1.58/1.81 1447[0:OCh:3.1,3.0,842.0,4.0] || -> equalish(add(u,v),add(add(w,u),subtract(v,w)))*r. % 1.58/1.81 2761[0:Res:1447.0,14.1] || equalish(add(b,subtract(a,b)),a)*l -> . % 1.58/1.81 2794[0:MRR:2761.0,23.0] || -> . % 1.58/1.81 % SZS output end Refutation % 1.58/1.81 Formulae used in the proof : prove_equation transitivity commutativity_of_addition associativity_of_addition addition_inverts_subtraction1 addition_inverts_subtraction2 commutativity1 commutativity2 add_substitution1 subtract_substitution1 % 1.58/1.81 %------------------------------------------------------------------------------