%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD069-1 : 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 97.47s 97.65s % Output : Refutation 97.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : FLD069-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.07/0.13 % 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 : Tue Jun 7 03:59:40 EDT 2022 % 0.13/0.34 % CPUTime : % 97.47/97.65 % 97.47/97.65 SPASS V 3.9 % 97.47/97.65 SPASS beiseite: Proof found. % 97.47/97.65 % SZS status Theorem % 97.47/97.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 97.47/97.65 SPASS derived 28562 clauses, backtracked 0 clauses, performed 0 splits and kept 17524 clauses. % 97.47/97.65 SPASS allocated 103314 KBytes. % 97.47/97.65 SPASS spent 0:1:35.12 on the problem. % 97.47/97.65 0:00:00.04 for the input. % 97.47/97.65 0:00:00.00 for the FLOTTER CNF translation. % 97.47/97.65 0:00:00.39 for inferences. % 97.47/97.65 0:00:00.00 for the backtracking. % 97.47/97.65 0:1:34.42 for the reduction. % 97.47/97.65 % 97.47/97.65 % 97.47/97.65 Here is a proof with depth 8, length 40 : % 97.47/97.65 % SZS output start Refutation % 97.47/97.65 2[0:Inp] || -> defined(b)*. % 97.47/97.65 3[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 97.47/97.65 4[0:Inp] || -> less_or_equal(additive_identity,b)*r. % 97.47/97.65 5[0:Inp] || equalish(b,additive_identity)*l -> . % 97.47/97.65 6[0:Inp] || -> equalish(add(a,b),additive_identity)*l. % 97.47/97.65 8[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 97.47/97.65 9[0:Inp] defined(u) || -> equalish(add(u,additive_inverse(u)),additive_identity)*l. % 97.47/97.65 17[0:Inp] || -> defined(additive_identity)*. % 97.47/97.65 18[0:Inp] defined(u) || -> defined(additive_inverse(u))*. % 97.47/97.65 22[0:Inp] || less_or_equal(u,v)*+ less_or_equal(v,u)* -> equalish(v,u). % 97.47/97.65 23[0:Inp] || less_or_equal(u,v)* less_or_equal(v,w)* -> less_or_equal(u,w)*. % 97.47/97.65 24[0:Inp] defined(u) defined(v) || -> less_or_equal(u,v)* less_or_equal(v,u)*. % 97.47/97.65 25[0:Inp] defined(u) || less_or_equal(v,w) -> less_or_equal(add(v,u),add(w,u))*. % 97.47/97.65 28[0:Inp] || equalish(u,v)* -> equalish(v,u). % 97.47/97.65 29[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 97.47/97.65 32[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 97.47/97.65 36[0:Res:4.0,22.0] || less_or_equal(b,additive_identity)*l -> equalish(additive_identity,b). % 97.47/97.65 45[0:Res:3.0,25.1] defined(u) || -> less_or_equal(add(additive_identity,u),add(a,u))*r. % 97.47/97.65 48[0:Res:28.1,5.0] || equalish(additive_identity,b)*r -> . % 97.47/97.65 50[0:Res:6.0,28.0] || -> equalish(additive_identity,add(a,b))*r. % 97.47/97.65 56[0:MRR:36.1,48.0] || less_or_equal(b,additive_identity)*l -> . % 97.47/97.65 82[0:Res:8.1,28.0] defined(u) || -> equalish(u,add(additive_identity,u))*r. % 97.47/97.65 98[0:OCh:29.1,29.0,82.1,9.1] defined(additive_inverse(additive_identity)) defined(additive_identity) || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 97.47/97.65 102[0:SSi:98.1,98.0,17.0,18.1,17.0] || -> equalish(additive_inverse(additive_identity),additive_identity)*l. % 97.47/97.65 116[0:Res:102.0,28.0] || -> equalish(additive_identity,additive_inverse(additive_identity))*r. % 97.47/97.65 205[0:Fac:24.2,24.3] defined(u) defined(u) || -> less_or_equal(u,u)*. % 97.47/97.65 262[0:Obv:205.0] defined(u) || -> less_or_equal(u,u)*. % 97.47/97.65 676[0:Res:50.0,32.0] || less_or_equal(additive_identity,u)*+ -> less_or_equal(add(a,b),u)*. % 97.47/97.65 679[0:Res:116.0,32.0] || less_or_equal(additive_identity,u)*+ -> less_or_equal(additive_inverse(additive_identity),u)*. % 97.47/97.65 684[0:Res:102.0,32.0] || less_or_equal(additive_inverse(additive_identity),u)* -> less_or_equal(additive_identity,u). % 97.47/97.65 693[0:Res:8.1,32.0] defined(u) || less_or_equal(add(additive_identity,u),v)* -> less_or_equal(u,v). % 97.47/97.65 912[0:Res:262.1,679.0] defined(additive_identity) || -> less_or_equal(additive_inverse(additive_identity),additive_identity)*l. % 97.47/97.65 928[0:SSi:912.0,17.0] || -> less_or_equal(additive_inverse(additive_identity),additive_identity)*l. % 97.47/97.65 965[0:Res:928.0,684.0] || -> less_or_equal(additive_identity,additive_identity)*. % 97.47/97.65 2354[0:Res:45.1,693.1] defined(u) defined(u) || -> less_or_equal(u,add(a,u))*r. % 97.47/97.65 2413[0:Obv:2354.0] defined(u) || -> less_or_equal(u,add(a,u))*r. % 97.47/97.65 36401[0:Res:965.0,676.0] || -> less_or_equal(add(a,b),additive_identity)*l. % 97.47/97.65 36531[0:OCh:23.1,23.0,36401.0,2413.1] defined(b) || -> less_or_equal(b,additive_identity)*l. % 97.47/97.65 36558[0:SSi:36531.0,2.0] || -> less_or_equal(b,additive_identity)*l. % 97.47/97.65 36559[0:MRR:36558.0,56.0] || -> . % 97.47/97.65 % SZS output end Refutation % 97.47/97.65 Formulae used in the proof : b_is_defined less_or_equal_3 less_or_equal_4 b_not_equal_to_additive_identity_5 add_equals_additive_identity_6 existence_of_identity_addition existence_of_inverse_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_order_relation % 97.47/97.65 %------------------------------------------------------------------------------