TSTP Solution File: HEN006-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 14.27s 14.47s
% Output : Refutation 14.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HEN006-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 1 14:56:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 14.27/14.47
% 14.27/14.47 SPASS V 3.9
% 14.27/14.47 SPASS beiseite: Proof found.
% 14.27/14.47 % SZS status Theorem
% 14.27/14.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.27/14.47 SPASS derived 19003 clauses, backtracked 0 clauses, performed 0 splits and kept 3176 clauses.
% 14.27/14.47 SPASS allocated 83540 KBytes.
% 14.27/14.47 SPASS spent 0:0:13.62 on the problem.
% 14.27/14.47 0:00:00.04 for the input.
% 14.27/14.47 0:00:00.00 for the FLOTTER CNF translation.
% 14.27/14.47 0:00:00.22 for inferences.
% 14.27/14.47 0:00:00.00 for the backtracking.
% 14.27/14.47 0:0:13.33 for the reduction.
% 14.27/14.47
% 14.27/14.47
% 14.27/14.47 Here is a proof with depth 11, length 48 :
% 14.27/14.47 % SZS output start Refutation
% 14.27/14.47 2[0:Inp] || -> equal(divide(zero,u),zero)**.
% 14.27/14.47 3[0:Inp] || -> equal(divide(u,u),zero)**.
% 14.27/14.47 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*.
% 14.27/14.47 6[0:Inp] || -> less_equal(divide(a,b),d)*l.
% 14.27/14.47 7[0:Inp] || less_equal(divide(a,d),b)*l -> .
% 14.27/14.47 8[0:Inp] || less_equal(u,v) -> equal(divide(u,v),zero)**.
% 14.27/14.47 9[0:Inp] || equal(divide(u,v),zero)** -> less_equal(u,v).
% 14.27/14.47 10[0:Inp] || -> less_equal(divide(u,v),u)*l.
% 14.27/14.47 11[0:Inp] || -> less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v))*l.
% 14.27/14.47 12[0:Inp] || -> less_equal(zero,u)*.
% 14.27/14.47 13[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u).
% 14.27/14.47 61[0:SpR:2.0,11.0] || -> less_equal(divide(divide(u,v),zero),divide(divide(u,zero),v))*.
% 14.27/14.47 63[0:SpR:3.0,11.0] || -> less_equal(divide(divide(u,v),zero),divide(divide(u,v),v))*.
% 14.27/14.47 64[0:SpR:8.1,11.0] || less_equal(u,v) -> less_equal(divide(divide(w,v),zero),divide(divide(w,u),v))*.
% 14.27/14.47 86[0:Res:12.0,13.0] || less_equal(u,zero)* -> equal(u,zero).
% 14.27/14.47 90[0:Res:10.0,13.0] || less_equal(u,divide(u,v))*r -> equal(divide(u,v),u).
% 14.27/14.47 140[0:NCh:5.2,5.0,86.0,11.0] || equal(divide(divide(u,v),w),zero) -> equal(divide(divide(u,w),divide(v,w)),zero)**.
% 14.27/14.47 367[0:SpR:3.0,61.0] || -> less_equal(divide(divide(u,divide(u,zero)),zero),zero)*l.
% 14.27/14.47 868[0:NCh:5.2,5.1,90.0,63.0] || less_equal(divide(u,v),divide(divide(u,v),zero))*r -> equal(divide(divide(u,v),v),divide(u,v))**.
% 14.27/14.47 1935[0:NCh:5.2,5.0,64.1,86.0] || less_equal(u,v) equal(divide(divide(w,u),v),zero)** -> equal(divide(divide(w,v),zero),zero)**.
% 14.27/14.47 2629[0:Res:367.0,86.0] || -> equal(divide(divide(u,divide(u,zero)),zero),zero)**.
% 14.27/14.47 2814[0:SpL:2629.0,9.0] || equal(zero,zero) -> less_equal(divide(u,divide(u,zero)),zero)*l.
% 14.27/14.47 2867[0:Obv:2814.0] || -> less_equal(divide(u,divide(u,zero)),zero)*l.
% 14.27/14.47 2949[0:Res:2867.0,86.0] || -> equal(divide(u,divide(u,zero)),zero)**.
% 14.27/14.47 3059[0:SpL:2949.0,9.0] || equal(zero,zero) -> less_equal(u,divide(u,zero))*r.
% 14.27/14.47 3087[0:Obv:3059.0] || -> less_equal(u,divide(u,zero))*r.
% 14.27/14.47 3088[0:MRR:868.0,3087.0] || -> equal(divide(divide(u,v),v),divide(u,v))**.
% 14.27/14.47 3301[0:SpR:3088.0,8.1] || less_equal(divide(u,v),v)*l -> equal(divide(u,v),zero).
% 14.27/14.47 3399[0:Res:3087.0,90.0] || -> equal(divide(u,zero),u)**.
% 14.27/14.47 3701[0:Rew:3399.0,1935.2] || less_equal(u,v) equal(divide(divide(w,u),v),zero)** -> equal(divide(w,v),zero).
% 14.27/14.47 4302[0:NCh:5.2,5.0,3301.0,10.0] || equal(u,v) -> equal(divide(u,v),zero)**.
% 14.27/14.47 7417[0:SpL:4302.1,3701.1] || equal(u,v)* less_equal(v,w)* equal(divide(zero,w),zero)** -> equal(divide(u,w),zero)**.
% 14.27/14.47 7451[0:Rew:2.0,7417.2] || equal(u,v)* less_equal(v,w)* equal(zero,zero) -> equal(divide(u,w),zero)**.
% 14.27/14.47 7452[0:Obv:7451.2] || equal(u,v)* less_equal(v,w)*+ -> equal(divide(u,w),zero)**.
% 14.27/14.47 11936[0:Res:6.0,7452.1] || equal(u,divide(a,b))*+ -> equal(divide(u,d),zero)**.
% 14.27/14.47 11937[0:Res:10.0,7452.1] || equal(u,divide(v,w))*+ -> equal(divide(u,v),zero)**.
% 14.27/14.47 11984[0:EqR:11936.0] || -> equal(divide(divide(a,b),d),zero)**.
% 14.27/14.47 12206[0:EqR:11937.0] || -> equal(divide(divide(u,v),u),zero)**.
% 14.27/14.47 12268[0:SpR:12206.0,140.1] || equal(divide(divide(u,divide(v,w)),v),zero)** -> equal(divide(divide(u,v),zero),zero).
% 14.27/14.47 12402[0:Rew:3399.0,12268.1] || equal(divide(divide(u,divide(v,w)),v),zero)** -> equal(divide(u,v),zero).
% 14.27/14.47 19034[0:SpL:140.1,12402.0] || equal(divide(divide(u,v),w),zero)** equal(divide(zero,v),zero) -> equal(divide(divide(u,w),v),zero)**.
% 14.27/14.47 19127[0:Rew:2.0,19034.1] || equal(divide(divide(u,v),w),zero)** equal(zero,zero) -> equal(divide(divide(u,w),v),zero)**.
% 14.27/14.47 19128[0:Obv:19127.1] || equal(divide(divide(u,v),w),zero)**+ -> equal(divide(divide(u,w),v),zero)**.
% 14.27/14.47 29806[0:SpL:11984.0,19128.0] || equal(zero,zero) -> equal(divide(divide(a,d),b),zero)**.
% 14.27/14.47 29833[0:Obv:29806.0] || -> equal(divide(divide(a,d),b),zero)**.
% 14.27/14.47 29972[0:SpL:29833.0,9.0] || equal(zero,zero) -> less_equal(divide(a,d),b)*l.
% 14.27/14.47 30122[0:Obv:29972.0] || -> less_equal(divide(a,d),b)*l.
% 14.27/14.47 30123[0:MRR:30122.0,7.0] || -> .
% 14.27/14.47 % SZS output end Refutation
% 14.27/14.47 Formulae used in the proof : zero_divide_anything_is_zero x_divide_x_is_zero transitivity_of_less_equal a_divide_b_LE_d prove_a_divide_d_LE_b quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 14.27/14.47
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