TSTP Solution File: SWC054-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC054-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 22:01:24 EDT 2022
% Result : Unsatisfiable 2.05s 2.23s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC054-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.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 : Sun Jun 12 02:15:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.05/2.23
% 2.05/2.23 SPASS V 3.9
% 2.05/2.23 SPASS beiseite: Proof found.
% 2.05/2.23 % SZS status Theorem
% 2.05/2.23 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.05/2.23 SPASS derived 4964 clauses, backtracked 2962 clauses, performed 88 splits and kept 5785 clauses.
% 2.05/2.23 SPASS allocated 80158 KBytes.
% 2.05/2.23 SPASS spent 0:00:01.88 on the problem.
% 2.05/2.23 0:00:00.04 for the input.
% 2.05/2.23 0:00:00.00 for the FLOTTER CNF translation.
% 2.05/2.23 0:00:00.03 for inferences.
% 2.05/2.23 0:00:00.03 for the backtracking.
% 2.05/2.23 0:00:01.58 for the reduction.
% 2.05/2.23
% 2.05/2.23
% 2.05/2.23 Here is a proof with depth 3, length 160 :
% 2.05/2.23 % SZS output start Refutation
% 2.05/2.23 1[0:Inp] || -> ssList(sk1)*.
% 2.05/2.23 4[0:Inp] || -> ssList(sk4)*.
% 2.05/2.23 5[0:Inp] || -> equal(sk2,sk4)**.
% 2.05/2.23 6[0:Inp] || -> equal(sk3,sk1)**.
% 2.05/2.23 7[0:Inp] || equal(nil,sk4)** -> equal(nil,sk3).
% 2.05/2.23 8[0:Inp] || neq(sk4,nil)* -> ssList(sk5).
% 2.05/2.23 9[0:Inp] || neq(sk4,nil) -> neq(sk5,nil)*.
% 2.05/2.23 10[0:Inp] || neq(sk4,nil) -> segmentP(sk4,sk5)*.
% 2.05/2.23 11[0:Inp] || neq(sk4,nil) -> segmentP(sk3,sk5)*.
% 2.05/2.23 12[0:Inp] || -> equal(nil,sk2) neq(sk2,nil)*.
% 2.05/2.23 13[0:Inp] ssList(u) || neq(u,nil) segmentP(sk2,u)* segmentP(sk1,u) -> equal(nil,sk2).
% 2.05/2.23 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 2.05/2.23 15[0:Inp] ssList(u) || equal(nil,sk1) neq(u,nil) segmentP(sk2,u)* segmentP(sk1,u) -> .
% 2.05/2.23 69[0:Inp] || equal(skac2,skac3)** -> .
% 2.05/2.23 71[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 2.05/2.23 72[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 2.05/2.23 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.05/2.23 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.05/2.23 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.05/2.23 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.05/2.23 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.05/2.23 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.05/2.23 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.05/2.23 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 2.05/2.23 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 2.05/2.23 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 2.05/2.23 95[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 2.05/2.23 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 2.05/2.23 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 2.05/2.23 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 2.05/2.23 132[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 2.05/2.23 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 2.05/2.23 172[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 2.05/2.23 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 2.05/2.23 192[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).
% 2.05/2.23 203[0:Rew:5.0,12.1,5.0,12.0] || -> neq(sk4,nil)* equal(nil,sk4).
% 2.05/2.23 204[0:Rew:5.0,14.1] || equal(nil,sk1) -> neq(sk4,nil)*.
% 2.05/2.23 205[0:Rew:6.0,11.1] || neq(sk4,nil) -> segmentP(sk1,sk5)*.
% 2.05/2.23 206[0:Rew:6.0,7.1] || equal(nil,sk4)** -> equal(nil,sk1).
% 2.05/2.23 207[0:Rew:5.0,13.4,5.0,13.2] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk4,u)* -> equal(nil,sk4).
% 2.05/2.23 208[0:Rew:5.0,15.3] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk4,u)* equal(nil,sk1) -> .
% 2.05/2.23 297[0:Res:4.0,71.0] || -> segmentP(sk4,nil)*.
% 2.05/2.23 417[0:Res:1.0,208.0] || equal(nil,sk1) neq(sk1,nil) segmentP(sk4,sk1)* segmentP(sk1,sk1) -> .
% 2.05/2.23 419[0:Res:1.0,207.0] || neq(sk1,nil) segmentP(sk4,sk1)* segmentP(sk1,sk1) -> equal(nil,sk4).
% 2.05/2.23 471[0:Res:1.0,72.0] || -> segmentP(sk1,sk1)*.
% 2.05/2.23 484[0:Res:1.0,192.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 2.05/2.23 513[0:Res:1.0,138.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 2.05/2.23 520[0:Res:1.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 2.05/2.23 525[0:Res:1.0,101.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 2.05/2.23 536[0:Res:1.0,172.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 2.05/2.23 567[0:MRR:419.2,471.0] || segmentP(sk4,sk1)* neq(sk1,nil) -> equal(nil,sk4).
% 2.05/2.23 572[0:Rew:567.2,417.0] || equal(sk4,sk1) neq(sk1,nil) segmentP(sk4,sk1)* segmentP(sk1,sk1) -> .
% 2.05/2.23 573[0:MRR:572.3,471.0] || segmentP(sk4,sk1)* neq(sk1,nil) equal(sk4,sk1) -> .
% 2.05/2.23 574[1:Spt:87.1] || -> ssItem(u)*.
% 2.05/2.23 577[1:MRR:525.0,574.0] || -> ssList(cons(u,sk1))*.
% 2.05/2.23 580[1:MRR:85.0,574.0] || -> cyclefreeP(cons(u,nil))*.
% 2.05/2.23 581[1:MRR:84.0,574.0] || -> totalorderP(cons(u,nil))*.
% 2.05/2.23 582[1:MRR:83.0,574.0] || -> strictorderP(cons(u,nil))*.
% 2.05/2.23 583[1:MRR:82.0,574.0] || -> totalorderedP(cons(u,nil))*.
% 2.05/2.23 584[1:MRR:81.0,574.0] || -> strictorderedP(cons(u,nil))*.
% 2.05/2.23 585[1:MRR:80.0,574.0] || -> duplicatefreeP(cons(u,nil))*.
% 2.05/2.23 586[1:MRR:79.0,574.0] || -> equalelemsP(cons(u,nil))*.
% 2.05/2.23 590[1:MRR:520.0,574.0] || -> equal(hd(cons(u,sk1)),u)**.
% 2.05/2.23 604[1:MRR:117.1,117.0,574.0] || -> equal(u,v) neq(u,v)*.
% 2.05/2.23 614[1:MRR:132.1,132.0,574.0] || neq(u,v)* equal(u,v) -> .
% 2.05/2.23 706[1:MRR:536.1,574.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 2.05/2.23 769[1:MRR:185.3,185.2,574.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 2.05/2.23 770[2:Spt:513.0,513.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 2.05/2.23 778[3:Spt:484.5] || -> equal(nil,sk1)**.
% 2.05/2.23 867[3:Rew:778.0,89.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 2.05/2.23 868[3:Rew:778.0,88.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 2.05/2.23 873[3:Rew:778.0,580.0] || -> cyclefreeP(cons(u,sk1))*.
% 2.05/2.23 874[3:Rew:778.0,581.0] || -> totalorderP(cons(u,sk1))*.
% 2.05/2.23 875[3:Rew:778.0,582.0] || -> strictorderP(cons(u,sk1))*.
% 2.05/2.23 876[3:Rew:778.0,583.0] || -> totalorderedP(cons(u,sk1))*.
% 2.05/2.23 877[3:Rew:778.0,584.0] || -> strictorderedP(cons(u,sk1))*.
% 2.05/2.23 878[3:Rew:778.0,585.0] || -> duplicatefreeP(cons(u,sk1))*.
% 2.05/2.23 879[3:Rew:778.0,586.0] || -> equalelemsP(cons(u,sk1))*.
% 2.05/2.23 934[3:Rew:867.1,770.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 2.05/2.23 957[3:Rew:868.1,706.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 2.05/2.23 1271[3:SpR:934.1,590.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 2.05/2.23 1278[3:SSi:1271.0,577.0,873.0,874.0,875.0,876.0,877.0,878.0,879.0] || -> equal(hd(sk1),u)*.
% 2.05/2.23 1340[3:Rew:1278.0,957.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 2.05/2.23 1497[3:Rew:1278.0,769.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 2.05/2.23 1609[3:Con:1497.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 2.05/2.23 1610[3:AED:69.0,1609.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 2.05/2.23 1611[3:Rew:1340.1,1610.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 2.05/2.23 1612[3:Obv:1611.1] ssList(u) || -> .
% 2.05/2.23 1613[3:UnC:1612.0,4.0] || -> .
% 2.05/2.23 1764[3:Spt:1613.0,484.5,778.0] || equal(nil,sk1)** -> .
% 2.05/2.23 1765[3:Spt:1613.0,484.0,484.1,484.2,484.3,484.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.05/2.23 1770[3:MRR:206.1,1764.0] || equal(nil,sk4)** -> .
% 2.05/2.23 1793[3:MRR:207.4,1770.0] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk4,u)* -> .
% 2.05/2.23 1796[4:Spt:8.0] || neq(sk4,nil)* -> .
% 2.05/2.23 1797[4:Res:604.1,1796.0] || -> equal(nil,sk4)**.
% 2.05/2.23 1798[4:MRR:1797.0,1770.0] || -> .
% 2.05/2.23 1799[4:Spt:1798.0,8.0,1796.0] || -> neq(sk4,nil)*.
% 2.05/2.23 1800[4:Spt:1798.0,8.1] || -> ssList(sk5)*.
% 2.05/2.23 1801[4:MRR:205.0,1799.0] || -> segmentP(sk1,sk5)*.
% 2.05/2.23 1802[4:MRR:10.0,1799.0] || -> segmentP(sk4,sk5)*.
% 2.05/2.23 1803[4:MRR:9.0,1799.0] || -> neq(sk5,nil)*.
% 2.05/2.23 2324[4:Res:1802.0,1793.3] ssList(sk5) || neq(sk5,nil) segmentP(sk1,sk5)* -> .
% 2.05/2.23 2329[4:SSi:2324.0,1800.0] || neq(sk5,nil) segmentP(sk1,sk5)* -> .
% 2.05/2.23 2330[4:MRR:2329.0,2329.1,1803.0,1801.0] || -> .
% 2.05/2.23 2332[2:Spt:2330.0,513.1] || -> equal(nil,sk1)**.
% 2.05/2.23 2339[2:Rew:2332.0,95.2] ssList(u) || segmentP(nil,u)* -> equal(sk1,u).
% 2.05/2.23 2416[2:Rew:2332.0,8.0] || neq(sk4,sk1)* -> ssList(sk5).
% 2.05/2.23 2431[2:Rew:2332.0,205.0] || neq(sk4,sk1) -> segmentP(sk1,sk5)*.
% 2.05/2.23 2433[2:Rew:2332.0,9.1,2332.0,9.0] || neq(sk4,sk1) -> neq(sk5,sk1)*.
% 2.05/2.23 2440[2:Rew:2332.0,204.1,2332.0,204.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 2.05/2.23 2441[2:Obv:2440.0] || -> neq(sk4,sk1)*.
% 2.05/2.23 2442[2:MRR:2416.0,2441.0] || -> ssList(sk5)*.
% 2.05/2.23 2443[2:MRR:2431.0,2441.0] || -> segmentP(sk1,sk5)*.
% 2.05/2.23 2445[2:MRR:2433.0,2441.0] || -> neq(sk5,sk1)*.
% 2.05/2.23 2487[2:Rew:2332.0,2339.1] ssList(u) || segmentP(sk1,u)* -> equal(sk1,u).
% 2.05/2.23 2574[2:Res:2445.0,614.0] || equal(sk5,sk1)** -> .
% 2.05/2.23 2657[2:Res:2443.0,2487.1] ssList(sk5) || -> equal(sk5,sk1)**.
% 2.05/2.23 2661[2:SSi:2657.0,2442.0] || -> equal(sk5,sk1)**.
% 2.05/2.23 2662[2:MRR:2661.0,2574.0] || -> .
% 2.05/2.23 2663[1:Spt:2662.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 2.05/2.23 2664[0:Rew:203.1,204.0] || equal(sk4,sk1) -> neq(sk4,nil)*.
% 2.05/2.23 5708[2:Spt:484.5] || -> equal(nil,sk1)**.
% 2.05/2.23 5711[2:Rew:5708.0,95.2] ssList(u) || segmentP(nil,u)* -> equal(sk1,u).
% 2.05/2.23 5730[2:Rew:5708.0,297.0] || -> segmentP(sk4,sk1)*.
% 2.05/2.23 5764[2:Rew:5708.0,2664.1] || equal(sk4,sk1) -> neq(sk4,sk1)*.
% 2.12/2.32 5765[2:Rew:5708.0,9.0] || neq(sk4,sk1) -> neq(sk5,nil)*.
% 2.12/2.32 5767[2:Rew:5708.0,205.0] || neq(sk4,sk1) -> segmentP(sk1,sk5)*.
% 2.12/2.32 5768[2:Rew:5708.0,203.0] || -> neq(sk4,sk1)* equal(nil,sk4).
% 2.12/2.32 5769[2:Rew:5708.0,8.0] || neq(sk4,sk1)* -> ssList(sk5).
% 2.12/2.32 5788[2:Rew:5708.0,567.2] || segmentP(sk4,sk1)* neq(sk1,nil) -> equal(sk4,sk1).
% 2.12/2.32 5815[2:Rew:5708.0,573.1] || segmentP(sk4,sk1)* neq(sk1,sk1) equal(sk4,sk1) -> .
% 2.12/2.32 5846[2:Rew:5708.0,5768.1] || -> neq(sk4,sk1)* equal(sk4,sk1).
% 2.12/2.32 5847[2:Rew:5846.1,5764.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 2.12/2.32 5848[2:Obv:5847.0] || -> neq(sk4,sk1)*.
% 2.12/2.32 5849[2:MRR:5769.0,5848.0] || -> ssList(sk5)*.
% 2.12/2.32 5850[2:Rew:5708.0,5765.1] || neq(sk4,sk1) -> neq(sk5,sk1)*.
% 2.12/2.32 5851[2:MRR:5850.0,5848.0] || -> neq(sk5,sk1)*.
% 2.12/2.32 5853[2:MRR:5767.0,5848.0] || -> segmentP(sk1,sk5)*.
% 2.12/2.32 5894[2:Rew:5708.0,5711.1] ssList(u) || segmentP(sk1,u)* -> equal(sk1,u).
% 2.12/2.32 5901[2:Rew:5708.0,5788.1] || segmentP(sk4,sk1)* neq(sk1,sk1) -> equal(sk4,sk1).
% 2.12/2.32 5902[2:MRR:5901.0,5730.0] || neq(sk1,sk1)* -> equal(sk4,sk1).
% 2.12/2.32 5905[2:Rew:5902.1,5815.2,5902.1,5815.0] || segmentP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 2.12/2.32 5906[2:Obv:5905.2] || segmentP(sk1,sk1)* neq(sk1,sk1) -> .
% 2.12/2.32 5907[2:MRR:5906.0,471.0] || neq(sk1,sk1)* -> .
% 2.12/2.32 6248[2:Res:5853.0,5894.1] ssList(sk5) || -> equal(sk5,sk1)**.
% 2.12/2.32 6252[2:SSi:6248.0,5849.0] || -> equal(sk5,sk1)**.
% 2.12/2.32 6254[2:Rew:6252.0,5851.0] || -> neq(sk1,sk1)*.
% 2.12/2.32 6257[2:MRR:6254.0,5907.0] || -> .
% 2.12/2.32 6258[2:Spt:6257.0,484.5,5708.0] || equal(nil,sk1)** -> .
% 2.12/2.32 6259[2:Spt:6257.0,484.0,484.1,484.2,484.3,484.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.12/2.32 6265[2:MRR:206.1,6258.0] || equal(nil,sk4)** -> .
% 2.12/2.32 6268[2:MRR:203.1,6265.0] || -> neq(sk4,nil)*.
% 2.12/2.32 6269[2:MRR:8.0,6268.0] || -> ssList(sk5)*.
% 2.12/2.32 6274[2:MRR:205.0,6268.0] || -> segmentP(sk1,sk5)*.
% 2.12/2.32 6275[2:MRR:10.0,6268.0] || -> segmentP(sk4,sk5)*.
% 2.12/2.32 6276[2:MRR:9.0,6268.0] || -> neq(sk5,nil)*.
% 2.12/2.32 6298[2:MRR:207.4,6265.0] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk4,u)* -> .
% 2.12/2.32 7008[2:Res:6275.0,6298.3] ssList(sk5) || neq(sk5,nil) segmentP(sk1,sk5)* -> .
% 2.12/2.32 7011[2:SSi:7008.0,6269.0] || neq(sk5,nil) segmentP(sk1,sk5)* -> .
% 2.12/2.32 7012[2:MRR:7011.0,7011.1,6276.0,6274.0] || -> .
% 2.12/2.32 % SZS output end Refutation
% 2.12/2.32 Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_12 co1_13 co1_14 co1_15 clause54 clause56 clause57 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause80 clause86 clause97 clause102 clause117 clause123 clause157 clause170 clause177
% 2.12/2.32
%------------------------------------------------------------------------------