%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD071-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n020.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 02:28:39 EDT 2022 % Result : Unsatisfiable 144.17s 144.42s % Output : Refutation 144.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : FLD071-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.08/0.14 % Command : run_spass %d %s % 0.15/0.36 % Computer : n020.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Tue Jun 7 02:52:07 EDT 2022 % 0.15/0.36 % CPUTime : % 144.17/144.42 % 144.17/144.42 SPASS V 3.9 % 144.17/144.42 SPASS beiseite: Proof found. % 144.17/144.42 % SZS status Theorem % 144.17/144.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 144.17/144.42 SPASS derived 30441 clauses, backtracked 0 clauses, performed 0 splits and kept 18864 clauses. % 144.17/144.42 SPASS allocated 105385 KBytes. % 144.17/144.42 SPASS spent 0:2:21.26 on the problem. % 144.17/144.42 0:00:00.03 for the input. % 144.17/144.42 0:00:00.00 for the FLOTTER CNF translation. % 144.17/144.42 0:00:00.46 for inferences. % 144.17/144.42 0:00:00.00 for the backtracking. % 144.17/144.42 0:2:20.43 for the reduction. % 144.17/144.42 % 144.17/144.42 % 144.17/144.42 Here is a proof with depth 5, length 47 : % 144.17/144.42 % SZS output start Refutation % 144.17/144.42 1[0:Inp] || -> defined(a)*. % 144.17/144.42 2[0:Inp] || -> defined(b)*. % 144.17/144.42 3[0:Inp] || -> defined(u__dfg)*. % 144.17/144.42 4[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 144.17/144.42 5[0:Inp] || -> less_or_equal(additive_identity,b)*r. % 144.17/144.42 6[0:Inp] || -> equalish(multiply(a,b),u__dfg)*l. % 144.17/144.42 7[0:Inp] || less_or_equal(additive_identity,u__dfg)*r -> . % 144.17/144.42 9[0:Inp] defined(u) || -> equalish(add(additive_identity,u),u)*l. % 144.17/144.42 11[0:Inp] defined(u) defined(v) || -> equalish(add(v,u),add(u,v))*. % 144.17/144.42 18[0:Inp] || -> defined(additive_identity)*. % 144.17/144.42 20[0:Inp] defined(u) defined(v) || -> defined(multiply(v,u))*. % 144.17/144.42 23[0:Inp] || less_or_equal(u,v)*+ less_or_equal(v,u)* -> equalish(v,u). % 144.17/144.42 25[0:Inp] defined(u) defined(v) || -> less_or_equal(u,v)* less_or_equal(v,u)*. % 144.17/144.42 27[0:Inp] || less_or_equal(additive_identity,u) less_or_equal(additive_identity,v) -> less_or_equal(additive_identity,multiply(v,u))*r. % 144.17/144.42 29[0:Inp] || equalish(u,v)* -> equalish(v,u). % 144.17/144.42 30[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 144.17/144.42 31[0:Inp] defined(u) || equalish(v,w) -> equalish(add(v,u),add(w,u))*. % 144.17/144.42 33[0:Inp] || equalish(u,v)*+ less_or_equal(u,w)* -> less_or_equal(v,w)*. % 144.17/144.42 38[0:Res:5.0,27.1] || less_or_equal(additive_identity,u) -> less_or_equal(additive_identity,multiply(u,b))*r. % 144.17/144.42 47[0:Res:25.2,7.0] defined(additive_identity) defined(u__dfg) || -> less_or_equal(u__dfg,additive_identity)*l. % 144.17/144.42 48[0:Res:33.2,7.0] || equalish(u,additive_identity)*+ less_or_equal(u,u__dfg)* -> . % 144.17/144.42 50[0:Res:6.0,29.0] || -> equalish(u__dfg,multiply(a,b))*r. % 144.17/144.42 54[0:MRR:47.0,47.1,18.0,3.0] || -> less_or_equal(u__dfg,additive_identity)*l. % 144.17/144.42 57[0:Res:4.0,38.0] || -> less_or_equal(additive_identity,multiply(a,b))*r. % 144.17/144.42 82[0:NCh:30.2,30.0,29.0,9.1] defined(u) || equalish(u,v)*+ -> equalish(v,add(additive_identity,u))*. % 144.17/144.42 134[0:NCh:30.2,30.0,11.2,29.0] defined(u) defined(v) || equalish(add(u,v),w)*+ -> equalish(w,add(v,u))*. % 144.17/144.42 194[0:Fac:25.2,25.3] defined(u) defined(u) || -> less_or_equal(u,u)*. % 144.17/144.42 265[0:Obv:194.0] defined(u) || -> less_or_equal(u,u)*. % 144.17/144.42 364[0:OCh:30.1,30.0,31.2,9.1] defined(u) defined(u) || equalish(v,additive_identity) -> equalish(add(v,u),u)*l. % 144.17/144.42 374[0:Obv:364.0] defined(u) || equalish(v,additive_identity) -> equalish(add(v,u),u)*l. % 144.17/144.42 561[0:Res:57.0,23.0] || less_or_equal(multiply(a,b),additive_identity)*l -> equalish(multiply(a,b),additive_identity). % 144.17/144.42 645[0:NCh:30.2,30.0,48.0,6.0] || equalish(u__dfg,additive_identity) less_or_equal(multiply(a,b),u__dfg)*l -> . % 144.17/144.42 677[0:Res:50.0,33.0] || less_or_equal(u__dfg,u)*+ -> less_or_equal(multiply(a,b),u)*. % 144.17/144.42 1863[0:Res:6.0,82.1] defined(multiply(a,b)) || -> equalish(u__dfg,add(additive_identity,multiply(a,b)))*r. % 144.17/144.42 1989[0:SSi:1863.0,20.0,1.0,2.2] || -> equalish(u__dfg,add(additive_identity,multiply(a,b)))*r. % 144.17/144.42 3299[0:Res:1989.0,29.0] || -> equalish(add(additive_identity,multiply(a,b)),u__dfg)*l. % 144.17/144.42 5061[0:Res:3299.0,134.2] defined(additive_identity) defined(multiply(a,b)) || -> equalish(u__dfg,add(multiply(a,b),additive_identity))*r. % 144.17/144.42 5166[0:SSi:5061.1,5061.0,20.0,1.0,2.0,18.2] || -> equalish(u__dfg,add(multiply(a,b),additive_identity))*r. % 144.17/144.42 6878[0:OCh:30.1,30.0,5166.0,374.2] defined(additive_identity) || equalish(multiply(a,b),additive_identity)*l -> equalish(u__dfg,additive_identity). % 144.17/144.42 6893[0:SSi:6878.0,18.0] || equalish(multiply(a,b),additive_identity)*l -> equalish(u__dfg,additive_identity). % 144.17/144.42 37958[0:Res:54.0,677.0] || -> less_or_equal(multiply(a,b),additive_identity)*l. % 144.17/144.42 37967[0:Res:265.1,677.0] defined(u__dfg) || -> less_or_equal(multiply(a,b),u__dfg)*l. % 144.17/144.42 38179[0:MRR:561.0,37958.0] || -> equalish(multiply(a,b),additive_identity)*l. % 144.17/144.42 38197[0:MRR:6893.0,38179.0] || -> equalish(u__dfg,additive_identity)*l. % 144.17/144.42 38199[0:MRR:645.0,38197.0] || less_or_equal(multiply(a,b),u__dfg)*l -> . % 144.17/144.42 38397[0:SSi:37967.0,3.0] || -> less_or_equal(multiply(a,b),u__dfg)*l. % 144.17/144.42 38398[0:MRR:38397.0,38199.0] || -> . % 144.17/144.42 % SZS output end Refutation % 144.17/144.42 Formulae used in the proof : a_is_defined b_is_defined u_is_defined less_or_equal_4 less_or_equal_5 multiply_equals_u_6 not_less_or_equal_7 existence_of_identity_addition commutativity_addition well_definedness_of_additive_identity well_definedness_of_multiplication antisymmetry_of_order_relation totality_of_order_relation compatibility_of_order_relation_and_multiplication symmetry_of_equality transitivity_of_equality compatibility_of_equality_and_addition compatibility_of_equality_and_order_relation % 144.17/144.42 %------------------------------------------------------------------------------