%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD070-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n028.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 02:28:38 EDT 2022 % Result : Unsatisfiable 0.61s 0.83s % Output : Refutation 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : FLD070-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.12/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n028.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 : Tue Jun 7 00:55:14 EDT 2022 % 0.13/0.34 % CPUTime : % 0.61/0.83 % 0.61/0.83 SPASS V 3.9 % 0.61/0.83 SPASS beiseite: Proof found. % 0.61/0.83 % SZS status Theorem % 0.61/0.83 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.61/0.83 SPASS derived 1608 clauses, backtracked 0 clauses, performed 0 splits and kept 931 clauses. % 0.61/0.83 SPASS allocated 77265 KBytes. % 0.61/0.83 SPASS spent 0:00:00.46 on the problem. % 0.61/0.83 0:00:00.04 for the input. % 0.61/0.83 0:00:00.00 for the FLOTTER CNF translation. % 0.61/0.83 0:00:00.03 for inferences. % 0.61/0.83 0:00:00.00 for the backtracking. % 0.61/0.83 0:00:00.36 for the reduction. % 0.61/0.83 % 0.61/0.83 % 0.61/0.83 Here is a proof with depth 4, length 32 : % 0.61/0.83 % SZS output start Refutation % 0.61/0.83 1[0:Inp] || -> defined(a)*. % 0.61/0.83 2[0:Inp] || -> defined(b)*. % 0.61/0.83 3[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 0.61/0.83 4[0:Inp] || -> less_or_equal(additive_identity,b)*r. % 0.61/0.83 5[0:Inp] || less_or_equal(additive_identity,add(a,b))*r -> . % 0.61/0.83 7[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 0.61/0.83 15[0:Inp] defined(u) defined(v) || -> defined(add(v,u))*. % 0.61/0.83 16[0:Inp] || -> defined(additive_identity)*. % 0.61/0.83 21[0:Inp] || less_or_equal(u,v)*+ less_or_equal(v,u)* -> equalish(v,u). % 0.61/0.83 22[0:Inp] || less_or_equal(u,v)* less_or_equal(v,w)* -> less_or_equal(u,w)*. % 0.61/0.83 23[0:Inp] defined(u) defined(v) || -> less_or_equal(u,v)* less_or_equal(v,u)*. % 0.61/0.83 24[0:Inp] defined(u) || less_or_equal(v,w) -> less_or_equal(add(v,u),add(w,u))*. % 0.61/0.83 28[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.61/0.83 31[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 0.61/0.83 37[0:Res:4.0,21.1] || less_or_equal(b,additive_identity)*l -> equalish(b,additive_identity). % 0.61/0.83 44[0:Res:3.0,24.1] defined(u) || -> less_or_equal(add(additive_identity,u),add(a,u))*r. % 0.61/0.83 45[0:Res:23.2,5.0] defined(additive_identity) defined(add(a,b)) || -> less_or_equal(add(a,b),additive_identity)*l. % 0.61/0.83 46[0:Res:31.2,5.0] || equalish(u,additive_identity)* less_or_equal(u,add(a,b))*+ -> . % 0.61/0.83 48[0:MRR:45.0,16.0] defined(add(a,b)) || -> less_or_equal(add(a,b),additive_identity)*l. % 0.61/0.83 65[0:SoR:48.0,15.2] defined(a) defined(b) || -> less_or_equal(add(a,b),additive_identity)*l. % 0.61/0.83 66[0:SSi:65.1,65.0,2.0,1.0] || -> less_or_equal(add(a,b),additive_identity)*l. % 0.61/0.83 67[0:OCh:22.1,22.0,44.1,66.0] defined(b) || -> less_or_equal(add(additive_identity,b),additive_identity)*l. % 0.61/0.83 69[0:SSi:67.0,2.0] || -> less_or_equal(add(additive_identity,b),additive_identity)*l. % 0.61/0.83 643[0:Res:7.1,31.0] defined(u) || less_or_equal(add(additive_identity,u),v)* -> less_or_equal(u,v). % 0.61/0.83 1280[0:Res:44.1,46.1] defined(b) || equalish(add(additive_identity,b),additive_identity)*l -> . % 0.61/0.83 1300[0:SSi:1280.0,2.0] || equalish(add(additive_identity,b),additive_identity)*l -> . % 0.61/0.83 1309[0:NCh:28.2,28.0,1300.0,7.1] defined(b) || equalish(b,additive_identity)*l -> . % 0.61/0.83 1311[0:SSi:1309.0,2.0] || equalish(b,additive_identity)*l -> . % 0.61/0.83 1312[0:MRR:37.1,1311.0] || less_or_equal(b,additive_identity)*l -> . % 0.61/0.83 1979[0:Res:69.0,643.1] defined(b) || -> less_or_equal(b,additive_identity)*l. % 0.61/0.83 2036[0:SSi:1979.0,2.0] || -> less_or_equal(b,additive_identity)*l. % 0.61/0.83 2037[0:MRR:2036.0,1312.0] || -> . % 0.61/0.83 % SZS output end Refutation % 0.61/0.83 Formulae used in the proof : a_is_defined b_is_defined less_or_equal_3 less_or_equal_4 not_less_or_equal_5 existence_of_identity_addition well_definedness_of_addition well_definedness_of_additive_identity antisymmetry_of_order_relation transitivity_of_order_relation totality_of_order_relation compatibility_of_order_relation_and_addition transitivity_of_equality compatibility_of_equality_and_order_relation % 0.61/0.83 %------------------------------------------------------------------------------