TSTP Solution File: SWC018-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC018-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 22:01:07 EDT 2022
% Result : Unsatisfiable 3.35s 3.59s
% Output : Refutation 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC018-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Sat Jun 11 19:33:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.35/3.59
% 3.35/3.59 SPASS V 3.9
% 3.35/3.59 SPASS beiseite: Proof found.
% 3.35/3.59 % SZS status Theorem
% 3.35/3.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.35/3.59 SPASS derived 7344 clauses, backtracked 4751 clauses, performed 81 splits and kept 8773 clauses.
% 3.35/3.59 SPASS allocated 82373 KBytes.
% 3.35/3.59 SPASS spent 0:00:03.23 on the problem.
% 3.35/3.59 0:00:00.04 for the input.
% 3.35/3.59 0:00:00.00 for the FLOTTER CNF translation.
% 3.35/3.59 0:00:00.04 for inferences.
% 3.35/3.59 0:00:00.08 for the backtracking.
% 3.35/3.59 0:00:02.87 for the reduction.
% 3.35/3.59
% 3.35/3.59
% 3.35/3.59 Here is a proof with depth 3, length 238 :
% 3.35/3.59 % SZS output start Refutation
% 3.35/3.59 1[0:Inp] || -> ssList(sk1)*.
% 3.35/3.59 2[0:Inp] || -> ssList(sk2)*.
% 3.35/3.59 5[0:Inp] || -> equal(sk4,sk2)**.
% 3.35/3.59 6[0:Inp] || -> equal(sk3,sk1)**.
% 3.35/3.59 7[0:Inp] || -> ssList(sk5)*.
% 3.35/3.59 8[0:Inp] || -> equal(app(sk3,sk5),sk4)**.
% 3.35/3.59 9[0:Inp] || -> equalelemsP(sk3)*.
% 3.35/3.59 11[0:Inp] || equal(nil,sk3)** -> equal(nil,sk4).
% 3.35/3.59 12[0:Inp] || -> neq(sk2,nil)* equal(nil,sk2).
% 3.35/3.59 13[0:Inp] ssList(u) || neq(u,nil) frontsegP(sk1,u) frontsegP(sk2,u)* -> equal(nil,sk2).
% 3.35/3.59 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 3.35/3.59 15[0:Inp] ssList(u) || equal(nil,sk1) neq(u,nil) frontsegP(sk2,u)* frontsegP(sk1,u) -> .
% 3.35/3.59 16[0:Inp] || -> equalelemsP(nil)*.
% 3.35/3.59 17[0:Inp] || -> duplicatefreeP(nil)*.
% 3.35/3.59 18[0:Inp] || -> strictorderedP(nil)*.
% 3.35/3.59 19[0:Inp] || -> totalorderedP(nil)*.
% 3.35/3.59 20[0:Inp] || -> strictorderP(nil)*.
% 3.35/3.59 21[0:Inp] || -> totalorderP(nil)*.
% 3.35/3.59 22[0:Inp] || -> cyclefreeP(nil)*.
% 3.35/3.59 23[0:Inp] || -> ssList(nil)*.
% 3.35/3.59 28[0:Inp] || -> ssList(skaf82(u))*.
% 3.35/3.59 69[0:Inp] || equal(skac2,skac3)** -> .
% 3.35/3.59 73[0:Inp] ssList(u) || -> rearsegP(u,nil)*.
% 3.35/3.59 74[0:Inp] ssList(u) || -> rearsegP(u,u)*.
% 3.35/3.59 76[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 3.35/3.59 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.35/3.59 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.35/3.59 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.35/3.59 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.35/3.59 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.35/3.59 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.35/3.59 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.35/3.59 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 3.35/3.59 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 3.35/3.59 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.35/3.59 97[0:Inp] ssList(u) || rearsegP(nil,u)* -> equal(nil,u).
% 3.35/3.59 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 3.35/3.59 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 3.35/3.59 115[0:Inp] ssList(u) ssList(v) || -> equal(u,v) neq(u,v)*.
% 3.35/3.59 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 3.35/3.59 133[0:Inp] ssList(u) ssList(v) || equal(app(u,v),nil)** -> equal(nil,u).
% 3.35/3.59 134[0:Inp] ssList(u) ssList(v) || equal(app(u,v),nil)** -> equal(nil,v).
% 3.35/3.59 135[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.35/3.59 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 3.35/3.59 143[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(u,v).
% 3.35/3.59 151[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(u,v) -> rearsegP(app(w,u),v)*.
% 3.35/3.59 152[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(u,v) -> frontsegP(app(u,w),v)*.
% 3.35/3.59 164[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 3.35/3.59 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.35/3.59 192[0:Inp] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(nil,v) equal(nil,u).
% 3.35/3.59 201[0:Rew:6.0,9.0] || -> equalelemsP(sk1)*.
% 3.35/3.59 204[0:Rew:6.0,8.0,5.0,8.0] || -> equal(app(sk1,sk5),sk2)**.
% 3.35/3.59 205[0:Rew:12.0,14.0] || equal(sk2,sk1) -> neq(sk2,nil)*.
% 3.35/3.59 206[0:Rew:5.0,11.1,6.0,11.0] || equal(nil,sk1)** -> equal(nil,sk2).
% 3.35/3.59 207[0:Rew:13.4,15.1] ssList(u) || neq(u,nil) frontsegP(sk1,u) frontsegP(sk2,u)* equal(sk2,sk1) -> .
% 3.35/3.59 244[0:Res:7.0,207.0] || frontsegP(sk1,sk5) frontsegP(sk2,sk5)* neq(sk5,nil) equal(sk2,sk1) -> .
% 3.35/3.59 286[0:Res:7.0,97.0] || rearsegP(nil,sk5)* -> equal(nil,sk5).
% 3.35/3.59 295[0:Res:7.0,89.0] || -> equal(app(nil,sk5),sk5)**.
% 3.35/3.59 296[0:Res:7.0,87.0] || -> ssItem(u)* duplicatefreeP(sk5)*.
% 3.35/3.59 299[0:Res:7.0,73.0] || -> rearsegP(sk5,nil)*.
% 3.35/3.59 300[0:Res:7.0,74.0] || -> rearsegP(sk5,sk5)*.
% 3.35/3.59 418[0:Res:2.0,164.0] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,app(v,sk2)))**.
% 3.35/3.59 419[0:Res:2.0,207.0] || equal(sk2,sk1) neq(sk2,nil) frontsegP(sk2,sk2)* frontsegP(sk1,sk2) -> .
% 3.35/3.59 421[0:Res:2.0,13.0] || neq(sk2,nil) frontsegP(sk2,sk2)* frontsegP(sk1,sk2) -> equal(nil,sk2).
% 3.35/3.59 471[0:Res:2.0,87.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 3.35/3.59 477[0:Res:2.0,76.0] || -> frontsegP(sk2,sk2)*.
% 3.35/3.59 486[0:Res:2.0,192.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 3.35/3.59 516[0:Res:2.0,138.1] ssList(u) || -> equal(nil,sk2) equal(hd(app(sk2,u)),hd(sk2))**.
% 3.35/3.59 523[0:Res:2.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk2)),u)**.
% 3.35/3.59 528[0:Res:2.0,101.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 3.35/3.59 567[0:MRR:421.0,421.1,12.1,477.0] || frontsegP(sk1,sk2)* -> equal(nil,sk2).
% 3.35/3.59 568[0:Rew:567.1,419.1] || equal(sk2,sk1) neq(sk2,sk2) frontsegP(sk2,sk2)* frontsegP(sk1,sk2) -> .
% 3.35/3.59 569[0:MRR:568.2,477.0] || neq(sk2,sk2) frontsegP(sk1,sk2)* equal(sk2,sk1) -> .
% 3.35/3.59 570[1:Spt:87.1] || -> ssItem(u)*.
% 3.35/3.59 573[1:MRR:528.0,570.0] || -> ssList(cons(u,sk2))*.
% 3.35/3.59 576[1:MRR:85.0,570.0] || -> cyclefreeP(cons(u,nil))*.
% 3.35/3.59 577[1:MRR:84.0,570.0] || -> totalorderP(cons(u,nil))*.
% 3.35/3.59 578[1:MRR:83.0,570.0] || -> strictorderP(cons(u,nil))*.
% 3.35/3.59 579[1:MRR:82.0,570.0] || -> totalorderedP(cons(u,nil))*.
% 3.35/3.59 580[1:MRR:81.0,570.0] || -> strictorderedP(cons(u,nil))*.
% 3.35/3.59 581[1:MRR:80.0,570.0] || -> duplicatefreeP(cons(u,nil))*.
% 3.35/3.59 582[1:MRR:79.0,570.0] || -> equalelemsP(cons(u,nil))*.
% 3.35/3.59 586[1:MRR:523.0,570.0] || -> equal(hd(cons(u,sk2)),u)**.
% 3.35/3.59 600[1:MRR:117.1,117.0,570.0] || -> equal(u,v) neq(u,v)*.
% 3.35/3.59 701[1:MRR:135.1,570.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.35/3.59 769[1:MRR:185.3,185.2,570.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.35/3.59 770[2:Spt:516.0,516.2] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 3.35/3.59 778[3:Spt:486.5] || -> equal(nil,sk2)**.
% 3.35/3.59 860[3:Rew:778.0,89.1] ssList(u) || -> equal(app(sk2,u),u)**.
% 3.35/3.59 861[3:Rew:778.0,88.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 3.35/3.59 866[3:Rew:778.0,576.0] || -> cyclefreeP(cons(u,sk2))*.
% 3.35/3.59 867[3:Rew:778.0,577.0] || -> totalorderP(cons(u,sk2))*.
% 3.35/3.59 868[3:Rew:778.0,578.0] || -> strictorderP(cons(u,sk2))*.
% 3.35/3.59 869[3:Rew:778.0,579.0] || -> totalorderedP(cons(u,sk2))*.
% 3.35/3.59 870[3:Rew:778.0,580.0] || -> strictorderedP(cons(u,sk2))*.
% 3.35/3.59 871[3:Rew:778.0,581.0] || -> duplicatefreeP(cons(u,sk2))*.
% 3.35/3.59 872[3:Rew:778.0,582.0] || -> equalelemsP(cons(u,sk2))*.
% 3.35/3.59 881[3:Rew:778.0,701.1] ssList(u) || -> equal(app(cons(v,sk2),u),cons(v,u))**.
% 3.35/3.59 927[3:Rew:860.1,770.1] ssList(u) || -> equal(hd(u),hd(sk2))*.
% 3.35/3.59 940[3:Rew:861.1,418.2] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,v))**.
% 3.35/3.59 1229[3:SpR:927.1,586.0] ssList(cons(u,sk2)) || -> equal(hd(sk2),u)*.
% 3.35/3.59 1234[3:SSi:1229.0,573.0,866.0,867.0,868.0,869.0,870.0,871.0,872.0] || -> equal(hd(sk2),u)*.
% 3.35/3.59 1297[3:Rew:1234.0,769.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk2))** -> equal(w,x)*.
% 3.35/3.59 1317[3:Rew:1234.0,881.1] ssList(u) || -> equal(app(hd(sk2),u),cons(v,u))*.
% 3.35/3.59 1342[3:Rew:1234.0,940.2] ssList(u) ssList(v) || -> equal(app(u,v),hd(sk2))**.
% 3.35/3.59 1347[3:Rew:1234.0,164.3] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),hd(sk2))**.
% 3.35/3.59 1425[3:Con:1297.1] ssList(u) || equal(cons(v,u),hd(sk2))** -> equal(v,w)*.
% 3.35/3.59 1426[3:AED:69.0,1425.2] ssList(u) || equal(cons(v,u),hd(sk2))** -> .
% 3.35/3.59 1431[3:Rew:1342.2,1347.3] ssList(u) ssList(v) ssList(w) || -> equal(app(hd(sk2),w),hd(sk2))**.
% 3.35/3.59 1432[3:Con:1431.0] ssList(u) || -> equal(app(hd(sk2),u),hd(sk2))**.
% 3.35/3.59 1433[3:Rew:1432.1,1317.1] ssList(u) || -> equal(cons(v,u),hd(sk2))**.
% 3.35/3.59 1434[3:MRR:1433.1,1426.1] ssList(u) || -> .
% 3.35/3.59 1435[3:UnC:1434.0,28.0] || -> .
% 3.35/3.59 1481[3:Spt:1435.0,486.5,778.0] || equal(nil,sk2)** -> .
% 3.35/3.59 1482[3:Spt:1435.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 3.35/3.59 1488[3:MRR:206.1,1481.0] || equal(nil,sk1)** -> .
% 3.35/3.59 1498[3:MRR:13.4,1481.0] ssList(u) || neq(u,nil) frontsegP(sk1,u) frontsegP(sk2,u)* -> .
% 3.35/3.59 2449[0:SpL:204.0,134.2] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk5).
% 3.35/3.59 2513[0:SpL:204.0,133.2] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk1).
% 3.35/3.59 3969[0:SpR:204.0,151.4] ssList(sk5) ssList(u) ssList(sk1) || rearsegP(sk5,u)* -> rearsegP(sk2,u).
% 3.35/3.59 3974[0:SpR:204.0,152.4] ssList(sk1) ssList(u) ssList(sk5) || frontsegP(sk1,u) -> frontsegP(sk2,u)*.
% 3.65/3.89 4404[0:SSi:3969.2,3969.0,201.0,1.0,7.0] ssList(u) || rearsegP(sk5,u)* -> rearsegP(sk2,u).
% 3.65/3.89 4405[0:SSi:3974.2,3974.0,7.0,201.0,1.0] ssList(u) || frontsegP(sk1,u) -> frontsegP(sk2,u)*.
% 3.65/3.89 4406[3:MRR:1498.3,4405.2] ssList(u) || neq(u,nil) frontsegP(sk1,u)* -> .
% 3.65/3.89 4447[3:Res:76.1,4406.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 4449[3:Obv:4447.0] ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 4450[3:SSi:4449.0,201.0,1.0] || neq(sk1,nil)* -> .
% 3.65/3.89 4453[3:Res:600.1,4450.0] || -> equal(nil,sk1)**.
% 3.65/3.89 4454[3:MRR:4453.0,1488.0] || -> .
% 3.65/3.89 4455[2:Spt:4454.0,516.1] || -> equal(nil,sk2)**.
% 3.65/3.89 4501[2:Rew:4455.0,88.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 3.65/3.89 4616[2:Rew:4455.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 4682[2:MRR:569.0,4616.1] || frontsegP(sk1,sk2)* equal(sk2,sk1) -> .
% 3.65/3.89 4686[2:Rew:4455.0,2449.3,4455.0,2449.2] ssList(sk1) ssList(sk5) || equal(sk2,sk2) -> equal(sk5,sk2)**.
% 3.65/3.89 4687[2:Obv:4686.2] ssList(sk1) ssList(sk5) || -> equal(sk5,sk2)**.
% 3.65/3.89 4688[2:SSi:4687.1,4687.0,7.0,201.0,1.0] || -> equal(sk5,sk2)**.
% 3.65/3.89 4694[2:Rew:4688.0,204.0] || -> equal(app(sk1,sk2),sk2)**.
% 3.65/3.89 4997[2:SpR:4501.1,4694.0] ssList(sk1) || -> equal(sk2,sk1)**.
% 3.65/3.89 4999[2:SSi:4997.0,201.0,1.0] || -> equal(sk2,sk1)**.
% 3.65/3.89 5008[2:Rew:4999.0,477.0] || -> frontsegP(sk1,sk1)*.
% 3.65/3.89 5188[2:Rew:4999.0,4682.1,4999.0,4682.0] || frontsegP(sk1,sk1)* equal(sk1,sk1) -> .
% 3.65/3.89 5189[2:Obv:5188.1] || frontsegP(sk1,sk1)* -> .
% 3.65/3.89 5190[2:MRR:5189.0,5008.0] || -> .
% 3.65/3.89 5231[1:Spt:5190.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 3.65/3.89 5232[0:SSi:2449.0,201.0,1.0] ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk5).
% 3.65/3.89 5233[0:MRR:5232.0,7.0] || equal(nil,sk2)** -> equal(nil,sk5).
% 3.65/3.89 5237[0:Rew:5233.1,2513.3] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(sk5,sk1).
% 3.65/3.89 5238[0:SSi:5237.0,201.0,1.0] ssList(sk5) || equal(nil,sk2)** -> equal(sk5,sk1).
% 3.65/3.89 5239[0:MRR:5238.0,7.0] || equal(nil,sk2)** -> equal(sk5,sk1).
% 3.65/3.89 5240[0:Rew:5239.1,5233.1] || equal(nil,sk2)** -> equal(nil,sk1).
% 3.65/3.89 5248[0:MRR:13.3,4405.2] ssList(u) || neq(u,nil) frontsegP(sk1,u)* -> equal(nil,sk2).
% 3.65/3.89 5276[2:Spt:471.0] || -> ssItem(u)*.
% 3.65/3.89 5304[2:MRR:117.1,117.0,5276.0] || -> equal(u,v) neq(u,v)*.
% 3.65/3.89 5476[3:Spt:486.5] || -> equal(nil,sk2)**.
% 3.65/3.89 5492[3:Rew:5476.0,295.0] || -> equal(app(sk2,sk5),sk5)**.
% 3.65/3.89 5528[3:Rew:5476.0,5240.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 3.65/3.89 5530[3:Rew:5476.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 5576[3:Rew:5476.0,244.2] || frontsegP(sk1,sk5) frontsegP(sk2,sk5)* neq(sk5,sk2) equal(sk2,sk1) -> .
% 3.65/3.89 5636[3:Obv:5528.0] || -> equal(nil,sk1)**.
% 3.65/3.89 5637[3:Rew:5476.0,5636.0] || -> equal(sk2,sk1)**.
% 3.65/3.89 5643[3:Rew:5637.0,477.0] || -> frontsegP(sk1,sk1)*.
% 3.65/3.89 5645[3:Rew:5637.0,204.0] || -> equal(app(sk1,sk5),sk1)**.
% 3.65/3.89 5738[3:Rew:5637.0,5492.0] || -> equal(app(sk1,sk5),sk5)**.
% 3.65/3.89 5755[3:Rew:5645.0,5738.0] || -> equal(sk5,sk1)**.
% 3.65/3.89 5886[3:Rew:5637.0,5530.1,5637.0,5530.0] || equal(sk1,sk1) -> neq(sk1,sk1)*.
% 3.65/3.89 5887[3:Obv:5886.0] || -> neq(sk1,sk1)*.
% 3.65/3.89 6048[3:Rew:5637.0,5576.3,5755.0,5576.2,5637.0,5576.2,5637.0,5576.1,5755.0,5576.1,5755.0,5576.0] || frontsegP(sk1,sk1)* frontsegP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 3.65/3.89 6049[3:Obv:6048.3] || frontsegP(sk1,sk1)* neq(sk1,sk1) -> .
% 3.65/3.89 6050[3:MRR:6049.0,6049.1,5643.0,5887.0] || -> .
% 3.65/3.89 6119[3:Spt:6050.0,486.5,5476.0] || equal(nil,sk2)** -> .
% 3.65/3.89 6120[3:Spt:6050.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 3.65/3.89 6126[3:MRR:206.1,6119.0] || equal(nil,sk1)** -> .
% 3.65/3.89 6136[3:MRR:5248.3,6119.0] ssList(u) || neq(u,nil) frontsegP(sk1,u)* -> .
% 3.65/3.89 6982[0:Res:300.0,4404.1] ssList(sk5) || -> rearsegP(sk2,sk5)*.
% 3.65/3.89 7008[3:Res:76.1,6136.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 7010[3:Obv:7008.0] ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 7011[3:SSi:7010.0,201.0,1.0] || neq(sk1,nil)* -> .
% 3.65/3.89 7013[3:Res:5304.1,7011.0] || -> equal(nil,sk1)**.
% 3.65/3.89 7014[3:MRR:7013.0,6126.0] || -> .
% 3.65/3.89 7015[2:Spt:7014.0,471.1] || -> duplicatefreeP(sk2)*.
% 3.65/3.89 7016[0:SSi:6982.0,7.0] || -> rearsegP(sk2,sk5)*.
% 3.65/3.89 7021[3:Spt:296.0] || -> ssItem(u)*.
% 3.65/3.89 7051[3:MRR:117.1,117.0,7021.0] || -> equal(u,v) neq(u,v)*.
% 3.65/3.89 7221[4:Spt:486.5] || -> equal(nil,sk2)**.
% 3.65/3.89 7244[4:Rew:7221.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 7305[4:Rew:7221.0,286.1] || rearsegP(nil,sk5)* -> equal(sk5,sk2).
% 3.65/3.89 7315[4:Rew:7221.0,5240.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 3.65/3.89 7322[4:Rew:7221.0,244.2] || frontsegP(sk1,sk5) frontsegP(sk2,sk5)* neq(sk5,sk2) equal(sk2,sk1) -> .
% 3.65/3.89 7376[4:Rew:7221.0,7305.0] || rearsegP(sk2,sk5)* -> equal(sk5,sk2).
% 3.65/3.89 7377[4:MRR:7376.0,7016.0] || -> equal(sk5,sk2)**.
% 3.65/3.89 7515[4:Obv:7315.0] || -> equal(nil,sk1)**.
% 3.65/3.89 7516[4:Rew:7221.0,7515.0] || -> equal(sk2,sk1)**.
% 3.65/3.89 7521[4:Rew:7516.0,477.0] || -> frontsegP(sk1,sk1)*.
% 3.65/3.89 7617[4:Rew:7516.0,7244.0] || equal(sk1,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 7618[4:Rew:7516.0,7377.0] || -> equal(sk5,sk1)**.
% 3.65/3.89 7632[4:Obv:7617.0] || -> neq(sk2,sk2)*.
% 3.65/3.89 7633[4:Rew:7516.0,7632.0] || -> neq(sk1,sk1)*.
% 3.65/3.89 7798[4:Rew:7516.0,7322.3,7618.0,7322.2,7516.0,7322.2,7516.0,7322.1,7618.0,7322.1,7618.0,7322.0] || frontsegP(sk1,sk1)* frontsegP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 3.65/3.89 7799[4:Obv:7798.3] || frontsegP(sk1,sk1)* neq(sk1,sk1) -> .
% 3.65/3.89 7800[4:MRR:7799.0,7799.1,7521.0,7633.0] || -> .
% 3.65/3.89 7908[4:Spt:7800.0,486.5,7221.0] || equal(nil,sk2)** -> .
% 3.65/3.89 7909[4:Spt:7800.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 3.65/3.89 7915[4:MRR:206.1,7908.0] || equal(nil,sk1)** -> .
% 3.65/3.89 7925[4:MRR:5248.3,7908.0] ssList(u) || neq(u,nil) frontsegP(sk1,u)* -> .
% 3.65/3.89 7954[0:Res:7016.0,143.2] ssList(sk2) ssList(sk5) || rearsegP(sk5,sk2)* -> equal(sk5,sk2).
% 3.65/3.89 8787[4:Res:76.1,7925.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 8789[4:Obv:8787.0] ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 8790[4:SSi:8789.0,201.0,1.0] || neq(sk1,nil)* -> .
% 3.65/3.89 8792[4:Res:7051.1,8790.0] || -> equal(nil,sk1)**.
% 3.65/3.89 8793[4:MRR:8792.0,7915.0] || -> .
% 3.65/3.89 8794[3:Spt:8793.0,296.1] || -> duplicatefreeP(sk5)*.
% 3.65/3.89 8795[2:SSi:7954.1,7954.0,7.0,2.0,7015.0] || rearsegP(sk5,sk2)* -> equal(sk5,sk2).
% 3.65/3.89 8796[4:Spt:486.5] || -> equal(nil,sk2)**.
% 3.65/3.89 8807[4:Rew:8796.0,299.0] || -> rearsegP(sk5,sk2)*.
% 3.65/3.89 8819[4:Rew:8796.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 8892[4:Rew:8796.0,5240.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 3.65/3.89 8919[4:Rew:8796.0,244.2] || frontsegP(sk1,sk5) frontsegP(sk2,sk5)* neq(sk5,sk2) equal(sk2,sk1) -> .
% 3.65/3.89 8929[4:MRR:8795.0,8807.0] || -> equal(sk5,sk2)**.
% 3.65/3.89 9090[4:Obv:8892.0] || -> equal(nil,sk1)**.
% 3.65/3.89 9091[4:Rew:8796.0,9090.0] || -> equal(sk2,sk1)**.
% 3.65/3.89 9097[4:Rew:9091.0,477.0] || -> frontsegP(sk1,sk1)*.
% 3.65/3.89 9192[4:Rew:9091.0,8929.0] || -> equal(sk5,sk1)**.
% 3.65/3.89 9198[4:Rew:9091.0,8819.0] || equal(sk1,sk1) -> neq(sk2,sk2)*.
% 3.65/3.89 9216[4:Obv:9198.0] || -> neq(sk2,sk2)*.
% 3.65/3.89 9217[4:Rew:9091.0,9216.0] || -> neq(sk1,sk1)*.
% 3.65/3.89 9374[4:Rew:9091.0,8919.3,9192.0,8919.2,9091.0,8919.2,9091.0,8919.1,9192.0,8919.1,9192.0,8919.0] || frontsegP(sk1,sk1)* frontsegP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 3.65/3.89 9375[4:Obv:9374.3] || frontsegP(sk1,sk1)* neq(sk1,sk1) -> .
% 3.65/3.89 9376[4:MRR:9375.0,9375.1,9097.0,9217.0] || -> .
% 3.65/3.89 9507[4:Spt:9376.0,486.5,8796.0] || equal(nil,sk2)** -> .
% 3.65/3.89 9508[4:Spt:9376.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 3.65/3.89 9516[4:MRR:206.1,9507.0] || equal(nil,sk1)** -> .
% 3.65/3.89 9524[4:MRR:5248.3,9507.0] ssList(u) || neq(u,nil) frontsegP(sk1,u)* -> .
% 3.65/3.89 10266[4:Res:76.1,9524.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 10268[4:Obv:10266.0] ssList(sk1) || neq(sk1,nil)* -> .
% 3.65/3.89 10269[4:SSi:10268.0,201.0,1.0] || neq(sk1,nil)* -> .
% 3.65/3.89 10416[4:Res:115.3,10269.0] ssList(sk1) ssList(nil) || -> equal(nil,sk1)**.
% 3.65/3.89 10420[4:SSi:10416.1,10416.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,201.0,1.0] || -> equal(nil,sk1)**.
% 3.65/3.89 10421[4:MRR:10420.0,9516.0] || -> .
% 3.65/3.89 % SZS output end Refutation
% 3.65/3.89 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_11 co1_12 co1_13 co1_14 co1_15 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause54 clause58 clause59 clause61 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause82 clause86 clause97 clause100 clause102 clause118 clause119 clause120 clause123 clause128 clause136 clause137 clause149 clause170 clause177
% 3.65/3.89
%------------------------------------------------------------------------------