%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD059-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n024.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 02:28:34 EDT 2022 % Result : Unsatisfiable 0.48s 0.69s % Output : Refutation 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : FLD059-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.00/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n024.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 : Mon Jun 6 15:44:05 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.69 % 0.48/0.69 SPASS V 3.9 % 0.48/0.69 SPASS beiseite: Proof found. % 0.48/0.69 % SZS status Theorem % 0.48/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.48/0.69 SPASS derived 1322 clauses, backtracked 0 clauses, performed 0 splits and kept 811 clauses. % 0.48/0.69 SPASS allocated 77048 KBytes. % 0.48/0.69 SPASS spent 0:00:00.33 on the problem. % 0.48/0.69 0:00:00.03 for the input. % 0.48/0.69 0:00:00.00 for the FLOTTER CNF translation. % 0.48/0.69 0:00:00.02 for inferences. % 0.48/0.69 0:00:00.00 for the backtracking. % 0.48/0.69 0:00:00.25 for the reduction. % 0.48/0.69 % 0.48/0.69 % 0.48/0.69 Here is a proof with depth 4, length 31 : % 0.48/0.69 % SZS output start Refutation % 0.48/0.69 1[0:Inp] || -> defined(a)*. % 0.48/0.69 2[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 0.48/0.69 3[0:Inp] || less_or_equal(additive_identity,add(a,a))*r -> . % 0.48/0.69 5[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 0.48/0.69 13[0:Inp] defined(u) defined(v) || -> defined(add(v,u))*. % 0.48/0.69 14[0:Inp] || -> defined(additive_identity)*. % 0.48/0.69 19[0:Inp] || less_or_equal(u,v)*+ less_or_equal(v,u)* -> equalish(v,u). % 0.48/0.69 20[0:Inp] || less_or_equal(u,v)* less_or_equal(v,w)* -> less_or_equal(u,w)*. % 0.48/0.69 21[0:Inp] defined(u) defined(v) || -> less_or_equal(u,v)* less_or_equal(v,u)*. % 0.48/0.69 22[0:Inp] defined(u) || less_or_equal(v,w) -> less_or_equal(add(v,u),add(w,u))*. % 0.48/0.69 26[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.48/0.69 29[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 0.48/0.69 35[0:Res:2.0,19.1] || less_or_equal(a,additive_identity)*l -> equalish(a,additive_identity). % 0.48/0.69 36[0:Res:2.0,22.1] defined(u) || -> less_or_equal(add(additive_identity,u),add(a,u))*r. % 0.48/0.69 37[0:Res:21.2,3.0] defined(additive_identity) defined(add(a,a)) || -> less_or_equal(add(a,a),additive_identity)*l. % 0.48/0.69 38[0:Res:29.2,3.0] || equalish(u,additive_identity)* less_or_equal(u,add(a,a))*+ -> . % 0.48/0.69 40[0:MRR:37.0,14.0] defined(add(a,a)) || -> less_or_equal(add(a,a),additive_identity)*l. % 0.48/0.69 50[0:SoR:40.0,13.2] defined(a) defined(a) || -> less_or_equal(add(a,a),additive_identity)*l. % 0.48/0.69 51[0:Obv:50.0] defined(a) || -> less_or_equal(add(a,a),additive_identity)*l. % 0.48/0.69 52[0:SSi:51.0,1.0] || -> less_or_equal(add(a,a),additive_identity)*l. % 0.48/0.69 53[0:OCh:20.1,20.0,36.1,52.0] defined(a) || -> less_or_equal(add(additive_identity,a),additive_identity)*l. % 0.48/0.69 55[0:SSi:53.0,1.0] || -> less_or_equal(add(additive_identity,a),additive_identity)*l. % 0.48/0.69 584[0:Res:5.1,29.0] defined(u) || less_or_equal(add(additive_identity,u),v)* -> less_or_equal(u,v). % 0.48/0.69 916[0:Res:36.1,38.1] defined(a) || equalish(add(additive_identity,a),additive_identity)*l -> . % 0.48/0.69 931[0:SSi:916.0,1.0] || equalish(add(additive_identity,a),additive_identity)*l -> . % 0.48/0.69 939[0:NCh:26.2,26.0,931.0,5.1] defined(a) || equalish(a,additive_identity)*l -> . % 0.48/0.69 941[0:SSi:939.0,1.0] || equalish(a,additive_identity)*l -> . % 0.48/0.69 942[0:MRR:35.1,941.0] || less_or_equal(a,additive_identity)*l -> . % 0.48/0.69 1658[0:Res:55.0,584.1] defined(a) || -> less_or_equal(a,additive_identity)*l. % 0.48/0.69 1696[0:SSi:1658.0,1.0] || -> less_or_equal(a,additive_identity)*l. % 0.48/0.69 1697[0:MRR:1696.0,942.0] || -> . % 0.48/0.69 % SZS output end Refutation % 0.48/0.69 Formulae used in the proof : a_is_defined less_or_equal_2 not_less_or_equal_3 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 % 0.48/0.69 %------------------------------------------------------------------------------