TSTP Solution File: HEN006-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 13:03:04 EDT 2022
% Result : Unsatisfiable 40.03s 40.21s
% Output : Refutation 40.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 13:11:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 40.03/40.21
% 40.03/40.21 SPASS V 3.9
% 40.03/40.21 SPASS beiseite: Proof found.
% 40.03/40.21 % SZS status Theorem
% 40.03/40.21 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.03/40.21 SPASS derived 63763 clauses, backtracked 0 clauses, performed 0 splits and kept 10284 clauses.
% 40.03/40.21 SPASS allocated 113872 KBytes.
% 40.03/40.21 SPASS spent 0:0:36.84 on the problem.
% 40.03/40.21 0:00:00.04 for the input.
% 40.03/40.21 0:00:00.00 for the FLOTTER CNF translation.
% 40.03/40.21 0:00:00.75 for inferences.
% 40.03/40.21 0:00:00.00 for the backtracking.
% 40.03/40.21 0:0:35.91 for the reduction.
% 40.03/40.21
% 40.03/40.21
% 40.03/40.21 Here is a proof with depth 11, length 69 :
% 40.03/40.21 % SZS output start Refutation
% 40.03/40.21 2[0:Inp] || -> quotient(zero,u,zero)*.
% 40.03/40.21 4[0:Inp] || -> quotient(u,zero,u)*.
% 40.03/40.21 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*.
% 40.03/40.21 6[0:Inp] || -> quotient(x__dfg,y__dfg,xQy)*.
% 40.03/40.21 7[0:Inp] || -> less_equal(xQy,z__dfg)*r.
% 40.03/40.21 8[0:Inp] || -> quotient(x__dfg,z__dfg,xQz)*.
% 40.03/40.21 9[0:Inp] || less_equal(xQz,y__dfg)*l -> .
% 40.03/40.21 10[0:Inp] || less_equal(u,v) -> quotient(u,v,zero)*.
% 40.03/40.21 11[0:Inp] || quotient(u,v,zero)* -> less_equal(u,v).
% 40.03/40.21 12[0:Inp] || quotient(u,v,w)* -> less_equal(w,u).
% 40.03/40.21 13[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)*.
% 40.03/40.22 14[0:Inp] || -> less_equal(zero,u)*.
% 40.03/40.22 15[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u).
% 40.03/40.22 17[0:Inp] || -> quotient(u,v,divide(u,v))*.
% 40.03/40.22 18[0:Inp] || quotient(u,v,w)*+ quotient(u,v,x)* -> equal(x,w)*.
% 40.03/40.22 19[0:Res:11.1,9.0] || quotient(xQz,y__dfg,zero)* -> .
% 40.03/40.22 40[0:Res:17.0,12.0] || -> less_equal(divide(u,v),u)*l.
% 40.03/40.22 51[0:Res:4.0,18.0] || quotient(u,zero,v)* -> equal(v,u).
% 40.03/40.22 52[0:Res:17.0,18.0] || quotient(u,v,w)* -> equal(w,divide(u,v)).
% 40.03/40.22 65[0:Res:14.0,15.0] || less_equal(u,zero)* -> equal(u,zero).
% 40.03/40.22 81[0:NCh:5.2,5.1,15.0,14.0] || equal(u,zero)* less_equal(v,u)*+ -> equal(v,u).
% 40.03/40.22 102[0:Res:2.0,13.0] || quotient(u,v,w)*+ quotient(x,y,u)* quotient(z,y,v)* quotient(x,z,zero)* -> less_equal(w,zero).
% 40.03/40.22 105[0:Res:4.0,13.0] || quotient(u,v,w)*+ quotient(x,zero,u)* quotient(y,zero,v)* quotient(x,y,z)* -> less_equal(w,z)*.
% 40.03/40.22 106[0:Res:17.0,13.0] || quotient(u,v,w)*+ quotient(x,y,u)* quotient(z,y,v)* quotient(x,z,x1)* -> less_equal(w,divide(x1,y))*.
% 40.03/40.22 107[0:Res:10.1,13.0] || less_equal(u,v)*+ quotient(w,x,y)* quotient(z,v,w)* quotient(x1,v,x)* quotient(z,x1,u)* -> less_equal(y,zero).
% 40.03/40.22 121[0:Res:17.0,51.0] || -> equal(divide(u,zero),u)**.
% 40.03/40.22 133[0:Res:40.0,15.0] || less_equal(u,divide(u,v))*r -> equal(divide(u,v),u).
% 40.03/40.22 148[0:Res:10.1,52.0] || less_equal(u,v) -> equal(divide(u,v),zero)**.
% 40.03/40.22 176[0:NCh:5.2,5.0,65.0,40.0] || equal(u,zero) -> equal(divide(u,v),zero)**.
% 40.03/40.22 191[0:SpR:176.1,17.0] || equal(u,zero) -> quotient(u,v,zero)*.
% 40.03/40.22 366[0:NCh:5.2,5.0,81.1,40.0] || equal(u,zero) equal(v,u) -> equal(divide(v,w),u)*.
% 40.03/40.22 514[0:SpR:366.2,17.0] || equal(u,zero) equal(v,u) -> quotient(v,w,u)*.
% 40.03/40.22 525[0:SpR:366.2,17.0] || equal(divide(u,v),zero) equal(w,divide(u,v)) -> quotient(u,v,divide(w,x))*.
% 40.03/40.22 829[0:Res:4.0,105.0] || quotient(u,zero,v)*+ quotient(w,zero,zero)* quotient(u,w,x)* -> less_equal(v,x)*.
% 40.03/40.22 886[0:Res:17.0,102.0] || quotient(u,v,w)*+ quotient(x,v,y)* quotient(u,x,zero)* -> less_equal(divide(w,y),zero)*l.
% 40.03/40.22 974[0:Res:17.0,106.0] || quotient(u,v,w)*+ quotient(x,v,y)* quotient(u,x,z)* -> less_equal(divide(w,y),divide(z,v))*.
% 40.03/40.22 999[0:Res:40.0,107.0] || quotient(u,v,w)* quotient(x,y,u)* quotient(z,y,v)* quotient(x,z,divide(y,x1))*+ -> less_equal(w,zero).
% 40.03/40.22 1179[0:SpL:366.2,133.0] || equal(u,zero)* equal(v,u) less_equal(v,u)* -> equal(divide(v,w),v)**.
% 40.03/40.22 2526[0:Res:4.0,829.0] || quotient(u,zero,zero)*+ quotient(v,u,w)* -> less_equal(v,w).
% 40.03/40.22 3187[0:Res:17.0,886.0] || quotient(u,v,w)*+ quotient(x,u,zero)* -> less_equal(divide(divide(x,v),w),zero)*l.
% 40.03/40.22 3319[0:Res:8.0,974.0] || quotient(u,z__dfg,v)*+ quotient(x__dfg,u,w)* -> less_equal(divide(xQz,v),divide(w,z__dfg))*.
% 40.03/40.22 3580[0:Res:4.0,999.3] || quotient(u,v,w)* quotient(divide(x,y),x,u)*+ quotient(zero,x,v)* -> less_equal(w,zero).
% 40.03/40.22 3714[0:Res:2.0,2526.0] || quotient(u,zero,v)* -> less_equal(u,v).
% 40.03/40.22 3718[0:Res:191.1,2526.0] || equal(u,zero) quotient(v,u,w)* -> less_equal(v,w).
% 40.03/40.22 3735[0:Res:514.2,3714.0] || equal(u,zero)*+ equal(v,u)* -> less_equal(v,u).
% 40.03/40.22 3739[0:MRR:1179.2,3735.2] || equal(u,zero)*+ equal(v,u)* -> equal(divide(v,w),v)**.
% 40.03/40.22 3766[0:Rew:3739.2,525.2] || equal(divide(u,v),zero) equal(w,divide(u,v)) -> quotient(u,v,w)*.
% 40.03/40.22 3884[0:Res:3766.2,19.0] || equal(divide(xQz,y__dfg),zero)** equal(divide(xQz,y__dfg),zero)** -> .
% 40.03/40.22 4027[0:Obv:3884.0] || equal(divide(xQz,y__dfg),zero)** -> .
% 40.03/40.22 4671[0:Res:17.0,3718.1] || equal(u,zero) -> less_equal(v,divide(v,u))*r.
% 40.03/40.22 4716[0:Res:4671.1,133.0] || equal(u,zero) -> equal(divide(v,u),v)**.
% 40.03/40.22 4918[0:SpR:4716.1,148.1] || equal(u,zero)* less_equal(v,u)*+ -> equal(v,zero)*.
% 40.03/40.22 7906[0:Res:17.0,3319.0] || quotient(x__dfg,u,v)*+ -> less_equal(divide(xQz,divide(u,z__dfg)),divide(v,z__dfg))*.
% 40.03/40.22 7991[0:Res:17.0,3187.0] || quotient(u,v,zero) -> less_equal(divide(divide(u,w),divide(v,w)),zero)*l.
% 40.03/40.22 11923[0:Res:17.0,3580.1] || quotient(divide(divide(u,v),u),w,x)* quotient(zero,u,w) -> less_equal(x,zero).
% 40.03/40.22 31039[0:Res:6.0,7906.0] || -> less_equal(divide(xQz,divide(y__dfg,z__dfg)),divide(xQy,z__dfg))*l.
% 40.03/40.22 32142[0:Res:31039.0,4918.1] || equal(divide(xQy,z__dfg),zero) -> equal(divide(xQz,divide(y__dfg,z__dfg)),zero)**.
% 40.03/40.22 32384[0:SpR:32142.1,17.0] || equal(divide(xQy,z__dfg),zero) -> quotient(xQz,divide(y__dfg,z__dfg),zero)*.
% 40.03/40.22 39669[0:Res:7991.1,65.0] || quotient(u,v,zero) -> equal(divide(divide(u,w),divide(v,w)),zero)**.
% 40.03/40.22 52299[0:Res:4.0,11923.0] || quotient(zero,u,zero) -> less_equal(divide(divide(u,v),u),zero)*l.
% 40.03/40.22 52320[0:MRR:52299.0,2.0] || -> less_equal(divide(divide(u,v),u),zero)*l.
% 40.03/40.22 52940[0:Res:52320.0,65.0] || -> equal(divide(divide(u,v),u),zero)**.
% 40.03/40.22 53317[0:SpR:52940.0,39669.1] || quotient(u,divide(v,w),zero)* -> equal(divide(divide(u,v),zero),zero).
% 40.03/40.22 53692[0:Rew:121.0,53317.1] || quotient(u,divide(v,w),zero)* -> equal(divide(u,v),zero).
% 40.03/40.22 82925[0:Res:32384.1,53692.0] || equal(divide(xQy,z__dfg),zero) -> equal(divide(xQz,y__dfg),zero)**.
% 40.03/40.22 82952[0:MRR:82925.1,4027.0] || equal(divide(xQy,z__dfg),zero)** -> .
% 40.03/40.22 82962[0:SpL:148.1,82952.0] || less_equal(xQy,z__dfg)*r equal(zero,zero) -> .
% 40.03/40.22 82975[0:Obv:82962.1] || less_equal(xQy,z__dfg)*r -> .
% 40.03/40.22 82976[0:MRR:82975.0,7.0] || -> .
% 40.03/40.22 % SZS output end Refutation
% 40.03/40.22 Formulae used in the proof : zero_divide_anything_is_zero x_divde_zero_is_x transitivity_of_less_equal xQy xQyLEz xQz prove_xQzLEy quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure well_defined
% 40.03/40.22
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