%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN007-2 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n007.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 13:03:06 EDT 2022 % Result : Unsatisfiable 2.14s 2.32s % Output : Refutation 2.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : HEN007-2 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n007.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 % 0.18/0.33 % CPULimit : 300 % 0.18/0.33 % WCLimit : 600 % 0.18/0.33 % DateTime : Fri Jul 1 13:08:39 EDT 2022 % 0.18/0.33 % CPUTime : % 2.14/2.32 % 2.14/2.32 SPASS V 3.9 % 2.14/2.32 SPASS beiseite: Proof found. % 2.14/2.32 % SZS status Theorem % 2.14/2.32 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 2.14/2.32 SPASS derived 9825 clauses, backtracked 0 clauses, performed 0 splits and kept 1760 clauses. % 2.14/2.32 SPASS allocated 71160 KBytes. % 2.14/2.32 SPASS spent 0:00:01.85 on the problem. % 2.14/2.32 0:00:00.04 for the input. % 2.14/2.32 0:00:00.00 for the FLOTTER CNF translation. % 2.14/2.32 0:00:00.12 for inferences. % 2.14/2.32 0:00:00.00 for the backtracking. % 2.14/2.32 0:00:01.65 for the reduction. % 2.14/2.32 % 2.14/2.32 % 2.14/2.32 Here is a proof with depth 4, length 18 : % 2.14/2.32 % SZS output start Refutation % 2.14/2.32 3[0:Inp] || -> quotient(u,u,zero)*. % 2.14/2.32 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*. % 2.14/2.32 6[0:Inp] || less_equal(u,v)*+ quotient(w,v,x)* quotient(w,y,u)* -> less_equal(x,y)*. % 2.14/2.32 7[0:Inp] || -> less_equal(x__dfg,y__dfg)*r. % 2.14/2.32 8[0:Inp] || -> quotient(z__dfg,y__dfg,zQy)*. % 2.14/2.32 9[0:Inp] || -> quotient(z__dfg,x__dfg,zQx)*. % 2.14/2.32 10[0:Inp] || less_equal(zQy,zQx)*r -> . % 2.14/2.32 12[0:Inp] || quotient(u,v,zero)* -> less_equal(u,v). % 2.14/2.32 18[0:Inp] || -> quotient(u,v,divide(u,v))*. % 2.14/2.32 22[0:Res:6.3,10.0] || less_equal(u,v)*+ quotient(w,v,zQy)* quotient(w,zQx,u)* -> . % 2.14/2.32 33[0:Res:3.0,12.0] || -> less_equal(u,u)*. % 2.14/2.32 106[0:Res:33.0,6.0] || quotient(u,v,w)*+ quotient(u,x,v)* -> less_equal(w,x)*. % 2.14/2.32 623[0:NCh:5.2,5.1,22.0,7.0] || less_equal(u,x__dfg) quotient(v,y__dfg,zQy) quotient(v,zQx,u)* -> . % 2.14/2.32 2557[0:Res:18.0,106.0] || quotient(u,v,w)* -> less_equal(divide(u,w),v). % 2.14/2.32 2928[0:Res:18.0,623.2] || less_equal(divide(u,zQx),x__dfg) quotient(u,y__dfg,zQy)* -> . % 2.14/2.32 2999[0:Res:9.0,2557.0] || -> less_equal(divide(z__dfg,zQx),x__dfg)*l. % 2.14/2.32 12876[0:Res:8.0,2928.1] || less_equal(divide(z__dfg,zQx),x__dfg)*l -> . % 2.14/2.32 12884[0:MRR:12876.0,2999.0] || -> . % 2.14/2.32 % SZS output end Refutation % 2.14/2.32 Formulae used in the proof : x_divide_x_is_zero transitivity_of_less_equal xQyLEz_implies_xQzLEy xLEy zQy zQx prove_zQyLEzQx less_equal_quotient closure % 2.14/2.32 %------------------------------------------------------------------------------