%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN010-7 : TPTP v8.1.0. Released v1.0.0. % 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 13:03:14 EDT 2022 % Result : Unsatisfiable 55.56s 55.75s % Output : Refutation 55.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN010-7 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.33 % Computer : n019.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Fri Jul 1 13:23:08 EDT 2022 % 0.13/0.34 % CPUTime : % 55.56/55.75 % 55.56/55.75 SPASS V 3.9 % 55.56/55.75 SPASS beiseite: Proof found. % 55.56/55.75 % SZS status Theorem % 55.56/55.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 55.56/55.75 SPASS derived 83505 clauses, backtracked 0 clauses, performed 0 splits and kept 11040 clauses. % 55.56/55.75 SPASS allocated 125402 KBytes. % 55.56/55.75 SPASS spent 0:0:50.20 on the problem. % 55.56/55.75 0:00:00.04 for the input. % 55.56/55.75 0:00:00.00 for the FLOTTER CNF translation. % 55.56/55.75 0:00:00.85 for inferences. % 55.56/55.75 0:00:00.00 for the backtracking. % 55.56/55.75 0:0:49.13 for the reduction. % 55.56/55.75 % 55.56/55.75 % 55.56/55.75 Here is a proof with depth 11, length 66 : % 55.56/55.75 % SZS output start Refutation % 55.56/55.75 3[0:Inp] || -> quotient(u,u,zero)*. % 55.56/55.75 4[0:Inp] || -> quotient(u,zero,u)*. % 55.56/55.75 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*. % 55.56/55.75 6[0:Inp] || less_equal(u,v)*+ quotient(w,v,x)* quotient(w,y,u)* -> less_equal(x,y)*. % 55.56/55.75 7[0:Inp] || less_equal(u,v)*+ quotient(w,u,x)* quotient(w,v,y)* -> less_equal(y,x)*. % 55.56/55.75 8[0:Inp] || less_equal(u,v)*+ quotient(v,w,x)* quotient(u,w,y)* -> less_equal(y,x)*. % 55.56/55.75 9[0:Inp] || -> quotient(identity,a,idQa)*. % 55.56/55.75 10[0:Inp] || -> quotient(identity,idQa,idQ_idQa)*. % 55.56/55.75 11[0:Inp] || -> quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa)*. % 55.56/55.75 12[0:Inp] || equal(idQa_Q__idQ_idQa,idQa)** -> . % 55.56/55.75 14[0:Inp] || quotient(u,v,zero)* -> less_equal(u,v). % 55.56/55.75 15[0:Inp] || quotient(u,v,w)* -> less_equal(w,u). % 55.56/55.75 16[0:Inp] || quotient(u,v,w)*+ quotient(x,y,z)* quotient(x1,v,x)* quotient(x2,v,y)* quotient(x1,x2,u)* -> less_equal(z,w)*. % 55.56/55.75 17[0:Inp] || -> less_equal(zero,u)*. % 55.56/55.75 18[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 55.56/55.75 19[0:Inp] || -> less_equal(u,identity)*. % 55.56/55.75 20[0:Inp] || -> quotient(u,v,divide(u,v))*. % 55.56/55.75 21[0:Inp] || quotient(u,v,w)*+ quotient(u,v,x)* -> equal(x,w)*. % 55.56/55.75 23[0:Res:18.2,12.0] || less_equal(idQa,idQa_Q__idQ_idQa) less_equal(idQa_Q__idQ_idQa,idQa)*l -> . % 55.56/55.75 31[0:Res:3.0,14.0] || -> less_equal(u,u)*. % 55.56/55.75 34[0:Res:11.0,15.0] || -> less_equal(idQa_Q__idQ_idQa,idQa)*l. % 55.56/55.75 41[0:Res:20.0,15.0] || -> less_equal(divide(u,v),u)*l. % 55.56/55.75 43[0:MRR:23.1,34.0] || less_equal(idQa,idQa_Q__idQ_idQa)*r -> . % 55.56/55.75 50[0:Res:3.0,21.0] || quotient(u,u,v)* -> equal(v,zero). % 55.56/55.75 51[0:Res:4.0,21.0] || quotient(u,zero,v)* -> equal(v,u). % 55.56/55.75 64[0:Res:17.0,18.0] || less_equal(u,zero)* -> equal(u,zero). % 55.56/55.75 94[0:Res:19.0,8.0] || quotient(identity,u,v)*+ quotient(w,u,x)* -> less_equal(x,v)*. % 55.56/55.75 121[0:Res:20.0,50.0] || -> equal(divide(u,u),zero)**. % 55.56/55.75 146[0:Res:20.0,51.0] || -> equal(divide(u,zero),u)**. % 55.56/55.75 157[0:Res:31.0,6.0] || quotient(u,v,w)*+ quotient(u,x,v)* -> less_equal(w,x)*. % 55.56/55.75 182[0:Res:20.0,16.0] || quotient(u,v,w)*+ quotient(x,y,u)* quotient(z,y,v)* quotient(x,z,x1)* -> less_equal(w,divide(x1,y))*. % 55.56/55.75 192[0:Res:41.0,7.0] || quotient(u,divide(v,w),x)*+ quotient(u,v,y)* -> less_equal(y,x)*. % 55.56/55.75 194[0:Res:41.0,18.0] || less_equal(u,divide(u,v))*r -> equal(divide(u,v),u). % 55.56/55.75 199[0:NCh:5.2,5.0,41.0,7.0] || equal(u,v)* quotient(w,divide(u,x),y)*+ quotient(w,v,z)* -> less_equal(z,y)*. % 55.56/55.75 518[0:Res:10.0,94.0] || quotient(u,idQa,v)* -> less_equal(v,idQ_idQa). % 55.56/55.75 519[0:Res:9.0,94.0] || quotient(u,a,v)* -> less_equal(v,idQa). % 55.56/55.75 545[0:Res:20.0,518.0] || -> less_equal(divide(u,idQa),idQ_idQa)*l. % 55.56/55.75 564[0:Res:545.0,18.0] || less_equal(idQ_idQa,divide(u,idQa))*r -> equal(divide(u,idQa),idQ_idQa). % 55.56/55.75 715[0:Res:20.0,519.0] || -> less_equal(divide(u,a),idQa)*l. % 55.56/55.75 743[0:Res:715.0,18.0] || less_equal(idQa,divide(u,a))*r -> equal(divide(u,a),idQa). % 55.56/55.75 3147[0:Res:4.0,182.0] || quotient(u,v,w)*+ quotient(x,v,zero)* quotient(u,x,y)* -> less_equal(w,divide(y,v))*. % 55.56/55.75 3148[0:Res:20.0,182.0] || quotient(u,v,w)*+ quotient(x,v,y)* quotient(u,x,z)* -> less_equal(divide(w,y),divide(z,v))*. % 55.56/55.75 7080[0:Res:20.0,157.0] || quotient(u,v,w)* -> less_equal(divide(u,w),v). % 55.56/55.75 8519[0:Res:20.0,192.0] || quotient(u,v,w)*+ -> less_equal(w,divide(u,divide(v,x)))*. % 55.56/55.75 13935[0:SpL:146.0,199.1] || equal(u,v)* quotient(w,u,x)*+ quotient(w,v,y)* -> less_equal(y,x)*. % 55.56/55.75 16872[0:Res:9.0,3147.0] || quotient(u,a,zero)*+ quotient(identity,u,v)* -> less_equal(idQa,divide(v,a)). % 55.56/55.75 17201[0:Res:20.0,7080.0] || -> less_equal(divide(u,divide(u,v)),v)*l. % 55.56/55.75 18544[0:Res:10.0,3148.0] || quotient(u,idQa,v)*+ quotient(identity,u,w)* -> less_equal(divide(idQ_idQa,v),divide(w,idQa))*. % 55.56/55.75 38998[0:Res:3.0,16872.0] || quotient(identity,a,u)* -> less_equal(idQa,divide(u,a)). % 55.56/55.75 49019[0:Res:20.0,18544.0] || quotient(identity,u,v)*+ -> less_equal(divide(idQ_idQa,divide(u,idQa)),divide(v,idQa))*. % 55.56/55.75 52005[0:Res:11.0,13935.1] || equal(idQ_idQa,u) quotient(idQa,u,v)* -> less_equal(v,idQa_Q__idQ_idQa). % 55.56/55.75 69171[0:Res:9.0,38998.0] || -> less_equal(idQa,divide(idQa,a))*r. % 55.56/55.75 69229[0:Res:69171.0,743.0] || -> equal(divide(idQa,a),idQa)**. % 55.56/55.75 69454[0:SpR:69229.0,20.0] || -> quotient(idQa,a,idQa)*. % 55.56/55.75 69745[0:Res:69454.0,8519.0] || -> less_equal(idQa,divide(idQa,divide(a,u)))*r. % 55.56/55.75 85320[0:Res:69745.0,194.0] || -> equal(divide(idQa,divide(a,u)),idQa)**. % 55.56/55.75 85549[0:SpR:85320.0,20.0] || -> quotient(idQa,divide(a,u),idQa)*. % 55.56/55.75 86791[0:Res:85549.0,52005.1] || equal(divide(a,u),idQ_idQa)** -> less_equal(idQa,idQa_Q__idQ_idQa). % 55.56/55.75 86807[0:MRR:86791.1,43.0] || equal(divide(a,u),idQ_idQa)** -> . % 55.56/55.75 113776[0:Res:9.0,49019.0] || -> less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa))*l. % 55.56/55.75 113806[0:Rew:121.0,113776.0] || -> less_equal(divide(idQ_idQa,divide(a,idQa)),zero)*l. % 55.56/55.75 113899[0:Res:113806.0,64.0] || -> equal(divide(idQ_idQa,divide(a,idQa)),zero)**. % 55.56/55.75 114125[0:SpR:113899.0,17201.0] || -> less_equal(divide(idQ_idQa,zero),divide(a,idQa))*l. % 55.56/55.75 114453[0:Rew:146.0,114125.0] || -> less_equal(idQ_idQa,divide(a,idQa))*r. % 55.56/55.75 115829[0:Res:114453.0,564.0] || -> equal(divide(a,idQa),idQ_idQa)**. % 55.56/55.75 115962[0:MRR:115829.0,86807.0] || -> . % 55.56/55.75 % SZS output end Refutation % 55.56/55.75 Formulae used in the proof : x_divide_x_is_zero x_divde_zero_is_x transitivity_of_less_equal xQyLEz_implies_xQzLEy xLEy_implies_zQyLEzQx xLEy_implies_xQzLEyQz identity_divide_a identity_divide_idQa identity_divide_idQ_idQa prove_idQa_equals_idQa_Q__idQ_idQa less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal identity_is_largest closure well_defined % 55.56/55.75 %------------------------------------------------------------------------------