%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD070-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n019.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 115.82s 115.99s % Output : Refutation 115.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : FLD070-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n019.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 : Mon Jun 6 16:56:55 EDT 2022 % 0.13/0.35 % CPUTime : % 115.82/115.99 % 115.82/115.99 SPASS V 3.9 % 115.82/115.99 SPASS beiseite: Proof found. % 115.82/115.99 % SZS status Theorem % 115.82/115.99 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 115.82/115.99 SPASS derived 30357 clauses, backtracked 0 clauses, performed 0 splits and kept 19126 clauses. % 115.82/115.99 SPASS allocated 105311 KBytes. % 115.82/115.99 SPASS spent 0:1:52.95 on the problem. % 115.82/115.99 0:00:00.04 for the input. % 115.82/115.99 0:00:00.00 for the FLOTTER CNF translation. % 115.82/115.99 0:00:00.44 for inferences. % 115.82/115.99 0:00:00.00 for the backtracking. % 115.82/115.99 0:1:52.18 for the reduction. % 115.82/115.99 % 115.82/115.99 % 115.82/115.99 Here is a proof with depth 7, length 60 : % 115.82/115.99 % SZS output start Refutation % 115.82/115.99 1[0:Inp] || -> defined(a)*. % 115.82/115.99 2[0:Inp] || -> defined(b)*. % 115.82/115.99 3[0:Inp] || -> defined(c)*. % 115.82/115.99 4[0:Inp] || -> equalish(add(a,b),c)*l. % 115.82/115.99 5[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 115.82/115.99 6[0:Inp] || -> less_or_equal(additive_identity,b)*r. % 115.82/115.99 7[0:Inp] || less_or_equal(additive_identity,c)*r -> . % 115.82/115.99 9[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 115.82/115.99 10[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 115.82/115.99 11[0:Inp] defined(u) defined(v) || -> equalish(add(v,u),add(u,v))*. % 115.82/115.99 17[0:Inp] defined(u) defined(v) || -> defined(add(v,u))*. % 115.82/115.99 18[0:Inp] || -> defined(additive_identity)*. % 115.82/115.99 19[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 115.82/115.99 23[0:Inp] || less_or_equal(u,v)*+ less_or_equal(v,u)* -> equalish(v,u). % 115.82/115.99 24[0:Inp] || less_or_equal(u,v)* less_or_equal(v,w)* -> less_or_equal(u,w)*. % 115.82/115.99 25[0:Inp] defined(u) defined(v) || -> less_or_equal(u,v)* less_or_equal(v,u)*. % 115.82/115.99 26[0:Inp] defined(u) || less_or_equal(v,w) -> less_or_equal(add(v,u),add(w,u))*. % 115.82/115.99 29[0:Inp] || equalish(u,v)* -> equalish(v,u). % 115.82/115.99 30[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 115.82/115.99 31[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*. % 115.82/115.99 33[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 115.82/115.99 36[0:Res:6.0,33.0] || equalish(additive_identity,u)*+ -> less_or_equal(u,b)*. % 115.82/115.99 46[0:Res:5.0,26.1] defined(u) || -> less_or_equal(add(additive_identity,u),add(a,u))*r. % 115.82/115.99 47[0:Res:25.2,7.0] defined(additive_identity) defined(c) || -> less_or_equal(c,additive_identity)*l. % 115.82/115.99 48[0:Res:33.2,7.0] || equalish(u,additive_identity) less_or_equal(u,c)* -> . % 115.82/115.99 50[0:Res:4.0,29.0] || -> equalish(c,add(a,b))*r. % 115.82/115.99 54[0:MRR:47.0,47.1,18.0,3.0] || -> less_or_equal(c,additive_identity)*l. % 115.82/115.99 79[0:Res:9.1,29.0] defined(u) || -> equalish(u,add(additive_identity,u))*r. % 115.82/115.99 83[0:NCh:30.2,30.0,29.0,9.1] defined(u) || equalish(u,v)*+ -> equalish(v,add(additive_identity,u))*. % 115.82/115.99 90[0:OCh:30.1,30.0,79.1,10.1] defined(additive_inverse(additive_identity)) defined(additive_identity) || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 115.82/115.99 94[0:SSi:90.1,90.0,18.0,19.1,18.0] || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 115.82/115.99 95[0:Res:94.0,29.0] || -> equalish(additive_identity,additive_inverse(additive_identity))*r. % 115.82/115.99 140[0:NCh:30.2,30.0,11.2,29.0] defined(u) defined(v) || equalish(add(u,v),w)*+ -> equalish(w,add(v,u))*. % 115.82/115.99 194[0:Fac:25.2,25.3] defined(u) defined(u) || -> less_or_equal(u,u)*. % 115.82/115.99 265[0:Obv:194.0] defined(u) || -> less_or_equal(u,u)*. % 115.82/115.99 328[0:Res:95.0,36.0] || -> less_or_equal(additive_inverse(additive_identity),b)*l. % 115.82/115.99 363[0:OCh:30.1,30.0,31.2,9.1] defined(u) defined(u) || equalish(v,additive_identity) -> equalish(add(v,u),u)*l. % 115.82/115.99 374[0:Obv:363.0] defined(u) || equalish(v,additive_identity) -> equalish(add(v,u),u)*l. % 115.82/115.99 639[0:Res:265.1,48.1] defined(c) || equalish(c,additive_identity)*l -> . % 115.82/115.99 659[0:SSi:639.0,3.0] || equalish(c,additive_identity)*l -> . % 115.82/115.99 672[0:Res:50.0,33.0] || less_or_equal(c,u)*+ -> less_or_equal(add(a,b),u)*. % 115.82/115.99 678[0:Res:9.1,33.0] defined(u) || less_or_equal(add(additive_identity,u),v)* -> less_or_equal(u,v). % 115.82/115.99 680[0:Res:94.0,33.0] || less_or_equal(additive_inverse(additive_identity),u)* -> less_or_equal(additive_identity,u). % 115.82/115.99 1004[0:NCh:24.2,24.0,680.0,328.0] || less_or_equal(b,u)* -> less_or_equal(additive_identity,u). % 115.82/115.99 1793[0:Res:4.0,83.1] defined(add(a,b)) || -> equalish(c,add(additive_identity,add(a,b)))*r. % 115.82/115.99 1927[0:SSi:1793.0,17.0,1.0,2.2] || -> equalish(c,add(additive_identity,add(a,b)))*r. % 115.82/115.99 2541[0:Res:46.1,678.1] defined(u) defined(u) || -> less_or_equal(u,add(a,u))*r. % 115.82/115.99 2589[0:Obv:2541.0] defined(u) || -> less_or_equal(u,add(a,u))*r. % 115.82/115.99 3159[0:Res:1927.0,29.0] || -> equalish(add(additive_identity,add(a,b)),c)*l. % 115.82/115.99 4956[0:Res:3159.0,140.2] defined(additive_identity) defined(add(a,b)) || -> equalish(c,add(add(a,b),additive_identity))*r. % 115.82/115.99 5118[0:SSi:4956.1,4956.0,17.0,1.0,2.0,18.2] || -> equalish(c,add(add(a,b),additive_identity))*r. % 115.82/115.99 7165[0:OCh:30.1,30.0,5118.0,374.2] defined(additive_identity) || equalish(add(a,b),additive_identity)*l -> equalish(c,additive_identity). % 115.82/115.99 7183[0:SSi:7165.0,18.0] || equalish(add(a,b),additive_identity)*l -> equalish(c,additive_identity). % 115.82/115.99 7184[0:MRR:7183.1,659.0] || equalish(add(a,b),additive_identity)*l -> . % 115.82/115.99 26712[0:Res:2589.1,1004.0] defined(b) || -> less_or_equal(additive_identity,add(a,b))*r. % 115.82/115.99 26792[0:SSi:26712.0,2.0] || -> less_or_equal(additive_identity,add(a,b))*r. % 115.82/115.99 26946[0:Res:26792.0,23.0] || less_or_equal(add(a,b),additive_identity)*l -> equalish(add(a,b),additive_identity). % 115.82/115.99 26997[0:MRR:26946.1,7184.0] || less_or_equal(add(a,b),additive_identity)*l -> . % 115.82/115.99 38533[0:Res:54.0,672.0] || -> less_or_equal(add(a,b),additive_identity)*l. % 115.82/115.99 38714[0:MRR:38533.0,26997.0] || -> . % 115.82/115.99 % SZS output end Refutation % 115.82/115.99 Formulae used in the proof : a_is_defined b_is_defined c_is_defined add_equals_c_4 less_or_equal_5 less_or_equal_6 not_less_or_equal_7 existence_of_identity_addition existence_of_inverse_addition commutativity_addition well_definedness_of_addition well_definedness_of_additive_identity well_definedness_of_additive_inverse antisymmetry_of_order_relation transitivity_of_order_relation totality_of_order_relation compatibility_of_order_relation_and_addition symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition compatibility_of_equality_and_order_relation % 115.82/115.99 %------------------------------------------------------------------------------