TSTP Solution File: SWV282-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV282-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Wed Jul 20 21:42:01 EDT 2022
% Result : Unsatisfiable 129.95s 130.14s
% Output : Refutation 132.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV282-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Wed Jun 15 13:08:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 129.95/130.14
% 129.95/130.14 SPASS V 3.9
% 129.95/130.14 SPASS beiseite: Proof found.
% 129.95/130.14 % SZS status Theorem
% 129.95/130.14 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.95/130.14 SPASS derived 21652 clauses, backtracked 7706 clauses, performed 13 splits and kept 19570 clauses.
% 129.95/130.14 SPASS allocated 88879 KBytes.
% 129.95/130.14 SPASS spent 0:02:09.77 on the problem.
% 129.95/130.14 0:00:00.04 for the input.
% 129.95/130.14 0:00:00.00 for the FLOTTER CNF translation.
% 129.95/130.14 0:00:00.67 for inferences.
% 129.95/130.14 0:00:00.74 for the backtracking.
% 129.95/130.14 0:02:08.26 for the reduction.
% 129.95/130.14
% 129.95/130.14
% 129.95/130.14 Here is a proof with depth 11, length 173 :
% 129.95/130.14 % SZS output start Refutation
% 129.95/130.14 1[0:Inp] || -> equal(c_Binomial_Obinomial(u,c_Suc(c_0)),u)**.
% 129.95/130.14 2[0:Inp] || -> equal(c_plus(c_Binomial_Obinomial(u,v),c_Binomial_Obinomial(u,c_Suc(v)),tc_nat),c_Binomial_Obinomial(c_Suc(u),c_Suc(v)))**.
% 129.95/130.14 3[0:Inp] || -> equal(c_Binomial_Obinomial(u,c_0),c_1)**.
% 129.95/130.14 4[0:Inp] || -> equal(c_Suc(c_0),c_1)**.
% 129.95/130.14 5[0:Inp] || equal(c_minus(u,v,tc_nat),c_0)** -> c_lessequals(u,v,tc_nat).
% 129.95/130.14 6[0:Inp] || -> equal(c_minus(u,u,tc_nat),c_0)**.
% 129.95/130.14 7[0:Inp] || -> c_lessequals(u,c_plus(u,v,tc_nat),tc_nat)*.
% 129.95/130.14 8[0:Inp] || -> c_less(u,c_Suc(u),tc_nat)*.
% 129.95/130.14 9[0:Inp] || c_lessequals(u,v,tc_nat) -> c_less(u,c_Suc(v),tc_nat)*.
% 129.95/130.14 10[0:Inp] || c_lessequals(c_plus(u,v,tc_nat),c_plus(u,w,tc_nat),tc_nat)* -> c_lessequals(v,w,tc_nat).
% 129.95/130.14 11[0:Inp] || c_less(c_plus(u,v,tc_nat),v,tc_nat)* -> .
% 129.95/130.14 12[0:Inp] || c_lessequals(v_sko__urX(u),v,tc_nat) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(u),tc_Message_Omsg)* -> .
% 129.95/130.14 14[0:Inp] || -> equal(u,v)* equal(v,w)* equal(u,w)* c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(w),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 129.95/130.14 15[0:Rew:4.0,1.0] || -> equal(c_Binomial_Obinomial(u,c_1),u)**.
% 129.95/130.14 22[0:SpR:4.0,9.1] || c_lessequals(u,c_0,tc_nat) -> c_less(u,c_1,tc_nat)*.
% 129.95/130.14 23[0:Res:9.1,11.0] || c_lessequals(c_plus(u,c_Suc(v),tc_nat),v,tc_nat)* -> .
% 129.95/130.14 24[0:Res:22.1,11.0] || c_lessequals(c_plus(u,c_1,tc_nat),c_0,tc_nat)* -> .
% 129.95/130.14 26[0:SpL:6.0,5.0] || equal(c_0,c_0) -> c_lessequals(u,u,tc_nat)*.
% 129.95/130.14 27[0:Obv:26.0] || -> c_lessequals(u,u,tc_nat)*.
% 129.95/130.14 28[0:SpR:2.0,7.0] || -> c_lessequals(c_Binomial_Obinomial(u,v),c_Binomial_Obinomial(c_Suc(u),c_Suc(v)),tc_nat)*.
% 129.95/130.14 30[0:SpR:4.0,2.0] || -> equal(c_plus(c_Binomial_Obinomial(u,c_0),c_Binomial_Obinomial(u,c_1),tc_nat),c_Binomial_Obinomial(c_Suc(u),c_1))**.
% 129.95/130.14 32[0:SpR:15.0,2.0] || -> equal(c_plus(u,c_Binomial_Obinomial(u,c_Suc(c_1)),tc_nat),c_Binomial_Obinomial(c_Suc(u),c_Suc(c_1)))**.
% 129.95/130.14 33[0:SpL:2.0,11.0] || c_less(c_Binomial_Obinomial(c_Suc(u),c_Suc(v)),c_Binomial_Obinomial(u,c_Suc(v)),tc_nat)* -> .
% 129.95/130.14 34[0:Rew:3.0,30.0,15.0,30.0,15.0,30.0] || -> equal(c_plus(c_1,u,tc_nat),c_Suc(u))**.
% 129.95/130.14 36[0:SpR:34.0,7.0] || -> c_lessequals(c_1,c_Suc(u),tc_nat)*.
% 129.95/130.14 38[0:SpL:34.0,11.0] || c_less(c_Suc(u),u,tc_nat)* -> .
% 129.95/130.14 39[0:SpL:34.0,24.0] || c_lessequals(c_Suc(c_1),c_0,tc_nat)* -> .
% 129.95/130.14 40[0:SpL:34.0,23.0] || c_lessequals(c_Suc(c_Suc(u)),u,tc_nat)* -> .
% 129.95/130.14 43[0:SpL:34.0,10.0] || c_lessequals(c_plus(c_1,u,tc_nat),c_Suc(v),tc_nat)* -> c_lessequals(u,v,tc_nat).
% 129.95/130.14 44[0:SpL:2.0,10.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(u),c_Suc(v)),c_plus(c_Binomial_Obinomial(u,v),w,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(u,c_Suc(v)),w,tc_nat).
% 129.95/130.14 47[0:Rew:34.0,43.0] || c_lessequals(c_Suc(u),c_Suc(v),tc_nat)* -> c_lessequals(u,v,tc_nat).
% 129.95/130.14 243[0:Res:14.4,12.1] || c_lessequals(v_sko__urX(v_evs_H),u,tc_nat)* -> equal(v,u)* equal(u,w)* equal(v,w)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(w),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 129.95/130.14 244[0:Res:14.5,12.1] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat)*+ -> equal(v,w)* equal(w,u)* equal(v,u)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(w),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 129.95/130.14 304[0:SpR:15.0,28.0] || -> c_lessequals(u,c_Binomial_Obinomial(c_Suc(u),c_Suc(c_1)),tc_nat)*.
% 129.95/130.14 435[0:SpR:32.0,34.0] || -> equal(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_1)),c_Suc(c_Binomial_Obinomial(c_1,c_Suc(c_1))))**.
% 129.95/130.14 444[0:SpL:32.0,10.0] || c_lessequals(c_plus(u,v,tc_nat),c_Binomial_Obinomial(c_Suc(u),c_Suc(c_1)),tc_nat)* -> c_lessequals(v,c_Binomial_Obinomial(u,c_Suc(c_1)),tc_nat).
% 129.95/130.14 452[0:SpL:435.0,33.0] || c_less(c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_1)),c_Suc(c_Binomial_Obinomial(c_1,c_Suc(c_1))),tc_nat)* -> .
% 129.95/130.14 468[0:Res:9.1,452.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_1)),c_Binomial_Obinomial(c_1,c_Suc(c_1)),tc_nat)* -> .
% 129.95/130.14 479[0:SpL:435.0,44.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_Suc(c_1))),c_plus(c_Suc(c_Binomial_Obinomial(c_1,c_Suc(c_1))),u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_Suc(c_1))),u,tc_nat).
% 129.95/130.14 707[0:Res:27.0,244.0] || -> equal(u,v)* equal(v,v_sko__urX(v_evs_H_H)) equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 129.95/130.14 929[0:Res:707.3,12.1] || c_lessequals(v_sko__urX(v_evs),u,tc_nat)* -> equal(u,v)* equal(v,v_sko__urX(v_evs_H_H)) equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 129.95/130.14 930[0:Res:707.4,12.1] || c_lessequals(v_sko__urX(v_evs_H),u,tc_nat)* -> equal(v,u)* equal(u,v_sko__urX(v_evs_H_H)) equal(v,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 949[0:Res:7.0,930.0] || -> equal(u,c_plus(v_sko__urX(v_evs_H),v,tc_nat))* equal(c_plus(v_sko__urX(v_evs_H),v,tc_nat),v_sko__urX(v_evs_H_H))** equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 950[0:Res:27.0,930.0] || -> equal(u,v_sko__urX(v_evs_H)) equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H_H)) equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 953[0:Res:27.0,243.0] || -> equal(u,v_sko__urX(v_evs_H)) equal(v_sko__urX(v_evs_H),v) equal(u,v)* c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 129.95/130.14 955[1:Spt:950.0,950.2,950.3] || -> equal(u,v_sko__urX(v_evs_H)) equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 968[1:Res:955.2,12.1] || c_lessequals(v_sko__urX(v_evs),u,tc_nat)* -> equal(u,v_sko__urX(v_evs_H)) equal(u,v_sko__urX(v_evs_H_H)).
% 129.95/130.14 969[1:Res:7.0,968.0] || -> equal(c_plus(v_sko__urX(v_evs),u,tc_nat),v_sko__urX(v_evs_H))** equal(c_plus(v_sko__urX(v_evs),u,tc_nat),v_sko__urX(v_evs_H_H)).
% 129.95/130.14 970[1:Res:27.0,968.0] || -> equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H))** equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H)).
% 129.95/130.14 972[2:Spt:970.0] || -> equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H))**.
% 129.95/130.14 976[2:Rew:972.0,969.0] || -> equal(c_plus(v_sko__urX(v_evs_H),u,tc_nat),v_sko__urX(v_evs_H)) equal(c_plus(v_sko__urX(v_evs),u,tc_nat),v_sko__urX(v_evs_H_H))**.
% 129.95/130.14 978[2:Rew:972.0,976.1] || -> equal(c_plus(v_sko__urX(v_evs_H),u,tc_nat),v_sko__urX(v_evs_H))** equal(c_plus(v_sko__urX(v_evs_H),u,tc_nat),v_sko__urX(v_evs_H_H)).
% 129.95/130.14 994[2:SpL:978.0,10.0] || c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H),u,tc_nat),tc_nat)* -> equal(c_plus(v_sko__urX(v_evs_H),v,tc_nat),v_sko__urX(v_evs_H_H))** c_lessequals(v,u,tc_nat)*.
% 129.95/130.14 1001[2:MRR:994.0,7.0] || -> equal(c_plus(v_sko__urX(v_evs_H),u,tc_nat),v_sko__urX(v_evs_H_H))** c_lessequals(u,v,tc_nat)*.
% 129.95/130.14 1012[2:SpL:1001.0,23.0] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat) -> c_lessequals(c_Suc(u),v,tc_nat)*.
% 129.95/130.14 1013[2:SpL:1001.0,10.0] || c_lessequals(c_plus(v_sko__urX(v_evs_H),u,tc_nat),v_sko__urX(v_evs_H_H),tc_nat)* -> c_lessequals(v,w,tc_nat)* c_lessequals(u,v,tc_nat)*.
% 129.95/130.14 1037[2:Rew:1001.0,1013.0] || c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat)* -> c_lessequals(u,v,tc_nat)* c_lessequals(w,u,tc_nat)*.
% 129.95/130.14 1038[2:MRR:1037.0,27.0] || -> c_lessequals(u,v,tc_nat)* c_lessequals(w,u,tc_nat)*.
% 129.95/130.14 1073[2:Res:1038.1,47.0] || -> c_lessequals(c_Suc(u),v,tc_nat)* c_lessequals(w,u,tc_nat)*.
% 129.95/130.14 1108[2:MRR:1012.0,1073.1] || -> c_lessequals(c_Suc(u),v,tc_nat)*.
% 129.95/130.14 1109[2:UnC:1108.0,40.0] || -> .
% 129.95/130.14 1110[2:Spt:1109.0,970.0,972.0] || equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H))** -> .
% 129.95/130.14 1111[2:Spt:1109.0,970.1] || -> equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H))**.
% 129.95/130.14 1114[2:Rew:1111.0,969.1,1111.0,969.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H))** equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H)).
% 129.95/130.14 1135[2:SpL:1114.0,11.0] || c_less(v_sko__urX(v_evs_H),u,tc_nat) -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))**.
% 129.95/130.14 1136[2:SpL:1114.0,10.0] || c_lessequals(v_sko__urX(v_evs_H),c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),tc_nat)* -> equal(c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),v_sko__urX(v_evs_H_H))** c_lessequals(v,u,tc_nat)*.
% 129.95/130.14 1139[2:SpL:1114.0,24.0] || c_lessequals(v_sko__urX(v_evs_H),c_0,tc_nat) -> equal(c_plus(v_sko__urX(v_evs_H_H),c_1,tc_nat),v_sko__urX(v_evs_H_H))**.
% 129.95/130.14 1151[2:SpL:1139.1,10.0] || c_lessequals(v_sko__urX(v_evs_H),c_0,tc_nat) c_lessequals(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H),tc_nat)* -> c_lessequals(u,c_1,tc_nat).
% 129.95/130.14 1209[2:SpL:1135.1,10.0] || c_less(v_sko__urX(v_evs_H),u,tc_nat)* c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),tc_nat)* -> c_lessequals(u,v,tc_nat)*.
% 129.95/130.14 1215[2:MRR:1209.1,7.0] || c_less(v_sko__urX(v_evs_H),u,tc_nat)*+ -> c_lessequals(u,v,tc_nat)*.
% 129.95/130.14 1216[2:Res:8.0,1215.0] || -> c_lessequals(c_Suc(v_sko__urX(v_evs_H)),u,tc_nat)*.
% 129.95/130.14 1220[2:Res:1216.0,47.0] || -> c_lessequals(v_sko__urX(v_evs_H),u,tc_nat)*.
% 129.95/130.14 1228[2:MRR:1136.0,1220.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))** c_lessequals(u,v,tc_nat)*.
% 129.95/130.14 1232[2:MRR:1151.0,1220.0] || c_lessequals(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H),tc_nat)* -> c_lessequals(u,c_1,tc_nat).
% 129.95/130.14 1237[2:Rew:1228.0,1232.0] || c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat)* -> c_lessequals(u,c_1,tc_nat)*.
% 129.95/130.14 1238[2:MRR:1237.0,27.0] || -> c_lessequals(u,c_1,tc_nat)*.
% 129.95/130.14 1239[2:UnC:1238.0,40.0] || -> .
% 129.95/130.14 1242[1:Spt:1239.0,950.1] || -> equal(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H_H))**.
% 129.95/130.14 1243[1:Rew:1242.0,953.1,1242.0,953.0] || -> equal(u,v_sko__urX(v_evs_H_H)) equal(v_sko__urX(v_evs_H_H),v) equal(u,v)* c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 129.95/130.14 1245[1:Rew:1242.0,949.1,1242.0,949.0] || -> equal(u,c_plus(v_sko__urX(v_evs_H_H),v,tc_nat))* equal(c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),v_sko__urX(v_evs_H_H))** equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 1263[1:SpR:1243.2,3.0] || -> equal(c_Binomial_Obinomial(u,c_0),v_sko__urX(v_evs_H_H)) equal(v_sko__urX(v_evs_H_H),v) c_in(c_Message_Omsg_ONonce(c_Binomial_Obinomial(u,c_0)),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)* equal(v,c_1).
% 129.95/130.14 1425[1:Res:1243.3,12.1] || c_lessequals(v_sko__urX(v_evs),u,tc_nat)*+ -> equal(u,v_sko__urX(v_evs_H_H)) equal(v_sko__urX(v_evs_H_H),v) equal(u,v)* c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 129.95/130.14 1430[1:Rew:3.0,1263.2,3.0,1263.0] || -> equal(v_sko__urX(v_evs_H_H),c_1) equal(v_sko__urX(v_evs_H_H),u) c_in(c_Message_Omsg_ONonce(c_1),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)* equal(u,c_1).
% 129.95/130.14 2052[2:Spt:1430.0] || -> equal(v_sko__urX(v_evs_H_H),c_1)**.
% 129.95/130.14 2125[2:Rew:2052.0,1245.2] || -> equal(u,c_plus(v_sko__urX(v_evs_H_H),v,tc_nat))* equal(c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),v_sko__urX(v_evs_H_H))** equal(u,c_1) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 2416[2:Rew:2052.0,2125.1,2052.0,2125.0] || -> equal(u,c_plus(c_1,v,tc_nat))* equal(c_plus(c_1,v,tc_nat),c_1)** equal(u,c_1) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 2417[2:Rew:34.0,2416.1,34.0,2416.0] || -> equal(u,c_Suc(v))* equal(c_Suc(v),c_1)** equal(u,c_1) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 129.95/130.14 2833[2:SpR:2417.0,36.0] || -> equal(c_Suc(u),c_1)** equal(v,c_1) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs),tc_Message_Omsg)* c_lessequals(c_1,v,tc_nat).
% 129.95/130.14 2963[2:Res:2417.3,12.1] || c_lessequals(v_sko__urX(v_evs),u,tc_nat)*+ -> equal(u,c_Suc(v))* equal(c_Suc(v),c_1)** equal(u,c_1).
% 129.95/130.14 2996[3:Spt:2833.0] || -> equal(c_Suc(u),c_1)**.
% 129.95/130.14 3006[3:Rew:2996.0,39.0] || c_lessequals(c_1,c_0,tc_nat)* -> .
% 129.95/130.14 3023[3:Rew:2996.0,34.0] || -> equal(c_plus(c_1,u,tc_nat),c_1)**.
% 129.95/130.14 3071[3:Rew:2996.0,479.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_Suc(c_1))),c_plus(c_1,u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_Suc(c_1))),u,tc_nat).
% 129.95/130.14 3739[3:Rew:2996.0,3071.1,2996.0,3071.1,2996.0,3071.0,3023.0,3071.0] || c_lessequals(c_Binomial_Obinomial(c_1,c_1),c_1,tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_1,c_1),u,tc_nat)*.
% 129.95/130.14 3740[3:Rew:15.0,3739.1,15.0,3739.0] || c_lessequals(c_1,c_1,tc_nat)* -> c_lessequals(c_1,u,tc_nat)*.
% 129.95/130.14 3741[3:MRR:3740.0,27.0] || -> c_lessequals(c_1,u,tc_nat)*.
% 129.95/130.14 3742[3:UnC:3741.0,3006.0] || -> .
% 129.95/130.14 4530[3:Spt:3742.0,2833.1,2833.2,2833.3] || -> equal(u,c_1) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs),tc_Message_Omsg)* c_lessequals(c_1,u,tc_nat).
% 129.95/130.14 4537[3:Res:4530.1,12.1] || c_lessequals(v_sko__urX(v_evs),u,tc_nat)* -> equal(u,c_1) c_lessequals(c_1,u,tc_nat).
% 129.95/130.14 4822[3:Res:27.0,4537.0] || -> equal(v_sko__urX(v_evs),c_1) c_lessequals(c_1,v_sko__urX(v_evs),tc_nat)*.
% 129.95/130.14 4824[4:Spt:4822.0] || -> equal(v_sko__urX(v_evs),c_1)**.
% 129.95/130.14 4826[4:Rew:4824.0,2963.0] || c_lessequals(c_1,u,tc_nat)*+ -> equal(u,c_Suc(v))* equal(c_Suc(v),c_1)** equal(u,c_1).
% 129.95/130.14 4900[4:Res:36.0,4826.0] || -> equal(c_Suc(u),c_Suc(v))* equal(c_Suc(v),c_1) equal(c_Suc(u),c_1).
% 129.95/130.14 4948[4:SpR:4900.0,8.0] || -> equal(c_Suc(u),c_1) equal(c_Suc(v),c_1) c_less(v,c_Suc(u),tc_nat)*.
% 129.95/130.14 5052[4:Res:4948.2,38.0] || -> equal(c_Suc(u),c_1) equal(c_Suc(c_Suc(c_Suc(u))),c_1)**.
% 129.95/130.14 5097[4:SpL:5052.1,40.0] || c_lessequals(c_1,c_Suc(u),tc_nat)* -> equal(c_Suc(u),c_1).
% 129.95/130.14 5103[4:MRR:5097.0,36.0] || -> equal(c_Suc(u),c_1)**.
% 129.95/130.14 5118[4:Rew:5103.0,39.0] || c_lessequals(c_1,c_0,tc_nat)* -> .
% 129.95/130.14 5125[4:Rew:5103.0,34.0] || -> equal(c_plus(c_1,u,tc_nat),c_1)**.
% 129.95/130.14 5326[4:Rew:5103.0,479.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_Suc(c_1))),c_plus(c_1,u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_Suc(c_1))),u,tc_nat).
% 129.95/130.14 5858[4:Rew:5103.0,5326.1,5103.0,5326.1,5103.0,5326.0,5125.0,5326.0] || c_lessequals(c_Binomial_Obinomial(c_1,c_1),c_1,tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_1,c_1),u,tc_nat)*.
% 129.95/130.14 5859[4:Rew:15.0,5858.1,15.0,5858.0] || c_lessequals(c_1,c_1,tc_nat)* -> c_lessequals(c_1,u,tc_nat)*.
% 129.95/130.14 5860[4:MRR:5859.0,27.0] || -> c_lessequals(c_1,u,tc_nat)*.
% 129.95/130.14 5861[4:UnC:5860.0,5118.0] || -> .
% 129.95/130.14 6645[4:Spt:5861.0,4822.0,4824.0] || equal(v_sko__urX(v_evs),c_1)** -> .
% 129.95/130.14 6646[4:Spt:5861.0,4822.1] || -> c_lessequals(c_1,v_sko__urX(v_evs),tc_nat)*.
% 129.95/130.14 7056[2:Res:27.0,2963.0] || -> equal(c_Suc(u),v_sko__urX(v_evs))** equal(c_Suc(u),c_1) equal(v_sko__urX(v_evs),c_1).
% 129.95/130.14 7058[4:MRR:7056.2,6645.0] || -> equal(c_Suc(u),v_sko__urX(v_evs))** equal(c_Suc(u),c_1).
% 129.95/130.14 7342[4:SpR:7058.0,8.0] || -> equal(c_Suc(u),c_1) c_less(u,v_sko__urX(v_evs),tc_nat)*.
% 129.95/130.14 7389[4:Res:7342.1,38.0] || -> equal(c_Suc(c_Suc(v_sko__urX(v_evs))),c_1)**.
% 129.95/130.14 7409[4:SpR:7058.0,7389.0] || -> equal(c_Suc(v_sko__urX(v_evs)),c_1)** equal(c_Suc(v_sko__urX(v_evs)),c_1)**.
% 129.95/130.14 7427[4:Obv:7409.0] || -> equal(c_Suc(v_sko__urX(v_evs)),c_1)**.
% 129.95/130.14 7429[4:Rew:7427.0,7389.0] || -> equal(c_Suc(c_1),c_1)**.
% 129.95/130.14 7456[4:Rew:7429.0,39.0] || c_lessequals(c_1,c_0,tc_nat)* -> .
% 129.95/130.14 7635[4:Rew:7429.0,479.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_1)),c_plus(c_Suc(c_Binomial_Obinomial(c_1,c_1)),u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_Suc(c_1))),u,tc_nat).
% 129.95/130.14 7916[4:Rew:15.0,7635.0] || c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_1)),c_plus(c_Suc(c_1),u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_Suc(c_1))),u,tc_nat).
% 129.95/130.14 7917[4:Rew:7429.0,7916.1,7429.0,7916.1,7429.0,7916.0] || c_lessequals(c_Binomial_Obinomial(c_1,c_1),c_plus(c_1,u,tc_nat),tc_nat)* -> c_lessequals(c_Binomial_Obinomial(c_1,c_1),u,tc_nat).
% 129.95/130.14 7918[4:Rew:15.0,7917.1,15.0,7917.0,34.0,7917.0] || c_lessequals(c_1,c_Suc(u),tc_nat)* -> c_lessequals(c_1,u,tc_nat).
% 132.45/132.62 7919[4:MRR:7918.0,36.0] || -> c_lessequals(c_1,u,tc_nat)*.
% 132.45/132.62 7920[4:UnC:7919.0,7456.0] || -> .
% 132.45/132.62 8353[2:Spt:7920.0,1430.0,2052.0] || equal(v_sko__urX(v_evs_H_H),c_1)** -> .
% 132.45/132.62 8354[2:Spt:7920.0,1430.1,1430.2,1430.3,1430.4] || -> equal(v_sko__urX(v_evs_H_H),u) c_in(c_Message_Omsg_ONonce(c_1),c_Event_Oused(v_evs),tc_Message_Omsg)* c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)* equal(u,c_1).
% 132.45/132.62 8355[3:Spt:8354.0,8354.2,8354.3] || -> equal(v_sko__urX(v_evs_H_H),u) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)* equal(u,c_1).
% 132.45/132.62 8370[3:Res:8355.1,12.1] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat)* -> equal(v_sko__urX(v_evs_H_H),u) equal(u,c_1).
% 132.45/132.62 8422[3:Res:7.0,8370.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))** equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),c_1).
% 132.45/132.62 8448[3:SpL:8422.0,10.0] || c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),tc_nat)* -> equal(c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),c_1)** c_lessequals(v,u,tc_nat)*.
% 132.45/132.62 8453[3:MRR:8448.0,7.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),c_1)** c_lessequals(u,v,tc_nat)*.
% 132.45/132.62 8462[3:SpL:8453.0,10.0] || c_lessequals(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),c_1,tc_nat)* -> c_lessequals(v,w,tc_nat)* c_lessequals(u,v,tc_nat)*.
% 132.45/132.62 8475[3:Rew:8453.0,8462.0] || c_lessequals(c_1,c_1,tc_nat)* -> c_lessequals(u,v,tc_nat)* c_lessequals(w,u,tc_nat)*.
% 132.45/132.62 8476[3:MRR:8475.0,27.0] || -> c_lessequals(u,v,tc_nat)* c_lessequals(w,u,tc_nat)*.
% 132.45/132.62 8495[3:Res:8476.0,468.0] || -> c_lessequals(u,c_Binomial_Obinomial(c_Suc(c_Suc(c_1)),c_Suc(c_1)),tc_nat)*.
% 132.45/132.62 8533[3:UnC:8495.0,40.0] || -> .
% 132.45/132.62 8534[3:Spt:8533.0,8354.1] || -> c_in(c_Message_Omsg_ONonce(c_1),c_Event_Oused(v_evs),tc_Message_Omsg)*.
% 132.45/132.62 8535[3:Res:8534.0,12.1] || c_lessequals(v_sko__urX(v_evs),c_1,tc_nat)* -> .
% 132.45/132.62 9096[1:Res:27.0,1425.0] || -> equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H)) equal(v_sko__urX(v_evs_H_H),u) equal(v_sko__urX(v_evs),u) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 132.45/132.62 9098[4:Spt:9096.1,9096.2,9096.3] || -> equal(v_sko__urX(v_evs_H_H),u) equal(v_sko__urX(v_evs),u) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)*.
% 132.45/132.62 9112[4:Res:9098.2,12.1] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat)* -> equal(v_sko__urX(v_evs_H_H),u) equal(v_sko__urX(v_evs),u).
% 132.45/132.62 9518[4:Res:7.0,9112.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H)) equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs))**.
% 132.45/132.62 9527[4:SpL:9518.1,11.0] || c_less(v_sko__urX(v_evs),u,tc_nat) -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))**.
% 132.45/132.62 11050[4:SpL:9527.1,10.0] || c_less(v_sko__urX(v_evs),u,tc_nat)* c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),tc_nat)* -> c_lessequals(u,v,tc_nat)*.
% 132.45/132.62 11056[4:MRR:11050.1,7.0] || c_less(v_sko__urX(v_evs),u,tc_nat)*+ -> c_lessequals(u,v,tc_nat)*.
% 132.45/132.62 11057[4:Res:8.0,11056.0] || -> c_lessequals(c_Suc(v_sko__urX(v_evs)),u,tc_nat)*.
% 132.45/132.62 11061[4:Res:11057.0,47.0] || -> c_lessequals(v_sko__urX(v_evs),u,tc_nat)*.
% 132.45/132.62 11068[4:UnC:11061.0,8535.0] || -> .
% 132.45/132.62 11069[4:Spt:11068.0,9096.0] || -> equal(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H))**.
% 132.45/132.62 11077[4:Rew:11069.0,929.0] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat)*+ -> equal(u,v)* equal(v,v_sko__urX(v_evs_H_H)) equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 132.45/132.62 14219[4:Res:7.0,11077.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v)* equal(v,v_sko__urX(v_evs_H_H)) equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))** c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 132.45/132.62 20822[4:SpL:14219.2,10.0] || c_lessequals(v_sko__urX(v_evs_H_H),c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),tc_nat)* -> equal(c_plus(v_sko__urX(v_evs_H_H),v,tc_nat),w)* equal(w,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(w),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_lessequals(v,u,tc_nat)*.
% 132.45/132.62 20833[4:MRR:20822.0,7.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v)* equal(v,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_lessequals(u,w,tc_nat)*.
% 132.45/132.62 21489[4:SpL:20833.0,11.0] || c_less(u,v,tc_nat)*+ -> equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_lessequals(v,w,tc_nat)*.
% 132.45/132.62 21563[4:Res:20833.3,40.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),c_Suc(c_Suc(u)),tc_nat),v)* equal(v,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(v),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 132.45/132.62 21787[4:SpL:21563.0,23.0] || c_lessequals(u,c_Suc(v),tc_nat)*+ -> equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 132.45/132.62 27062[4:Res:8.0,21489.0] || -> equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_lessequals(c_Suc(u),v,tc_nat)*.
% 132.45/132.62 27126[4:Res:27062.2,47.0] || -> equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H),tc_Message_Omsg)* c_lessequals(u,v,tc_nat)*.
% 132.45/132.62 27127[4:MRR:21787.0,27126.2] || -> equal(u,v_sko__urX(v_evs_H_H)) c_in(c_Message_Omsg_ONonce(u),c_Event_Oused(v_evs_H),tc_Message_Omsg)*.
% 132.45/132.62 27529[4:Res:27127.1,12.1] || c_lessequals(v_sko__urX(v_evs_H),u,tc_nat)* -> equal(u,v_sko__urX(v_evs_H_H)).
% 132.45/132.62 27530[4:Rew:1242.0,27529.0] || c_lessequals(v_sko__urX(v_evs_H_H),u,tc_nat)* -> equal(u,v_sko__urX(v_evs_H_H)).
% 132.45/132.62 28042[4:Res:7.0,27530.0] || -> equal(c_plus(v_sko__urX(v_evs_H_H),u,tc_nat),v_sko__urX(v_evs_H_H))**.
% 132.45/132.62 28044[4:Res:304.0,27530.0] || -> equal(c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H_H)),c_Suc(c_1)),v_sko__urX(v_evs_H_H))**.
% 132.45/132.62 28111[4:SpL:28042.0,444.0] || c_lessequals(v_sko__urX(v_evs_H_H),c_Binomial_Obinomial(c_Suc(v_sko__urX(v_evs_H_H)),c_Suc(c_1)),tc_nat)* -> c_lessequals(u,c_Binomial_Obinomial(v_sko__urX(v_evs_H_H),c_Suc(c_1)),tc_nat)*.
% 132.45/132.62 28124[4:Rew:28044.0,28111.0] || c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat) -> c_lessequals(u,c_Binomial_Obinomial(v_sko__urX(v_evs_H_H),c_Suc(c_1)),tc_nat)*.
% 132.45/132.62 28125[4:MRR:28124.0,27.0] || -> c_lessequals(u,c_Binomial_Obinomial(v_sko__urX(v_evs_H_H),c_Suc(c_1)),tc_nat)*.
% 132.45/132.62 28126[4:UnC:28125.0,40.0] || -> .
% 132.45/132.62 % SZS output end Refutation
% 132.45/132.62 Formulae used in the proof : cls_Binomial_Obinomial__1_0 cls_Binomial_Obinomial__Suc__Suc_0 cls_Binomial_Obinomial__n__0_0 cls_Nat_OOne__nat__def_0 cls_Nat_Odiff__is__0__eq_0 cls_Nat_Odiff__self__eq__0_0 cls_Nat_Ole__add1_0 cls_Nat_OlessI_0 cls_Nat_Oless__Suc__eq__le_1 cls_Nat_Onat__add__left__cancel__le_0 cls_Nat_Onot__add__less2_0 cls_Public_ONonce__supply__lemma_0 cls_conjecture_0
% 132.45/132.62
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