TSTP Solution File: HEN011-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN011-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 13:03:15 EDT 2022
% Result : Unsatisfiable 2.56s 2.76s
% Output : Refutation 2.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN011-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 14:15:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.56/2.76
% 2.56/2.76 SPASS V 3.9
% 2.56/2.76 SPASS beiseite: Proof found.
% 2.56/2.76 % SZS status Theorem
% 2.56/2.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.56/2.76 SPASS derived 8525 clauses, backtracked 0 clauses, performed 0 splits and kept 1831 clauses.
% 2.56/2.76 SPASS allocated 70602 KBytes.
% 2.56/2.76 SPASS spent 0:00:02.36 on the problem.
% 2.56/2.76 0:00:00.04 for the input.
% 2.56/2.76 0:00:00.00 for the FLOTTER CNF translation.
% 2.56/2.76 0:00:00.08 for inferences.
% 2.56/2.76 0:00:00.00 for the backtracking.
% 2.56/2.76 0:00:02.21 for the reduction.
% 2.56/2.76
% 2.56/2.76
% 2.56/2.76 Here is a proof with depth 3, length 25 :
% 2.56/2.76 % SZS output start Refutation
% 2.56/2.76 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*.
% 2.56/2.76 6[0:Inp] || less_equal(divide(u,v),w)*+ -> less_equal(divide(u,w),v)*.
% 2.56/2.76 7[0:Inp] || less_equal(u,v) -> less_equal(divide(w,v),divide(w,u))*.
% 2.56/2.76 9[0:Inp] || -> equal(divide(identity,divide(identity,divide(identity,u))),divide(identity,u))**.
% 2.56/2.76 10[0:Inp] || -> equal(divide(divide(identity,u),divide(identity,divide(identity,u))),divide(identity,u))**.
% 2.56/2.76 11[0:Inp] || equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b))))** -> .
% 2.56/2.76 14[0:Inp] || -> less_equal(divide(u,v),u)*l.
% 2.56/2.76 15[0:Inp] || -> less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v))*l.
% 2.56/2.76 17[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u).
% 2.56/2.76 20[0:Res:17.2,11.0] || less_equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b))))*l less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) -> .
% 2.56/2.76 120[0:SpR:10.0,15.0] || -> less_equal(divide(divide(identity,u),divide(v,divide(identity,divide(identity,u)))),divide(divide(divide(identity,u),v),divide(identity,divide(identity,u))))*r.
% 2.56/2.76 210[0:Res:14.0,17.0] || less_equal(u,divide(u,v))*r -> equal(divide(u,v),u).
% 2.56/2.76 218[0:NCh:5.2,5.0,17.0,14.0] || less_equal(u,v) less_equal(v,divide(u,w))* -> equal(v,divide(u,w)).
% 2.56/2.76 510[0:Res:15.0,6.0] || -> less_equal(divide(divide(u,v),divide(divide(u,w),v)),divide(w,v))*l.
% 2.56/2.76 512[0:Res:7.1,6.0] || less_equal(u,v)*+ -> less_equal(divide(w,divide(w,u)),v)*.
% 2.56/2.76 2658[0:SpR:9.0,510.0] || -> less_equal(divide(divide(identity,u),divide(divide(identity,v),divide(identity,divide(identity,u)))),divide(v,divide(identity,divide(identity,u))))*l.
% 2.56/2.76 4996[0:Res:14.0,512.0] || -> less_equal(divide(u,divide(u,divide(v,w))),v)*l.
% 2.56/2.76 5822[0:Res:4996.0,6.0] || -> less_equal(divide(u,v),divide(u,divide(v,w)))*r.
% 2.56/2.76 12555[0:Res:120.0,218.1] || less_equal(divide(divide(identity,u),v),divide(divide(identity,u),divide(v,divide(identity,divide(identity,u))))) -> equal(divide(divide(divide(identity,u),v),divide(identity,divide(identity,u))),divide(divide(identity,u),divide(v,divide(identity,divide(identity,u)))))**.
% 2.56/2.76 12588[0:NCh:5.2,5.1,120.0,210.0] || less_equal(divide(divide(identity,u),v),divide(divide(identity,u),divide(v,divide(identity,divide(identity,u))))) -> equal(divide(divide(divide(identity,u),v),divide(identity,divide(identity,u))),divide(divide(identity,u),v))**.
% 2.56/2.76 12692[0:MRR:12588.0,5822.0] || -> equal(divide(divide(divide(identity,u),v),divide(identity,divide(identity,u))),divide(divide(identity,u),v))**.
% 2.56/2.76 12728[0:Rew:12692.0,12555.1] || less_equal(divide(divide(identity,u),v),divide(divide(identity,u),divide(v,divide(identity,divide(identity,u)))))*r -> equal(divide(divide(identity,u),divide(v,divide(identity,divide(identity,u)))),divide(divide(identity,u),v)).
% 2.56/2.76 12729[0:MRR:12728.0,5822.0] || -> equal(divide(divide(identity,u),divide(v,divide(identity,divide(identity,u)))),divide(divide(identity,u),v))**.
% 2.56/2.76 12771[0:Rew:12729.0,2658.0] || -> less_equal(divide(divide(identity,u),divide(identity,v)),divide(v,divide(identity,divide(identity,u))))*.
% 2.56/2.76 12792[0:MRR:20.1,20.0,12771.0] || -> .
% 2.56/2.76 % SZS output end Refutation
% 2.56/2.76 Formulae used in the proof : transitivity_of_less_equal property_of_divide1 property_of_divide2 one_inversion_equals_three property_of_inversion prove_this quotient_smaller_than_numerator quotient_property less_equal_and_equal
% 2.56/2.76
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