TSTP Solution File: SWC200-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC200-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 22:02:25 EDT 2022
% Result : Unsatisfiable 4.40s 4.58s
% Output : Refutation 4.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC200-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 06:11:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.40/4.58
% 4.40/4.58 SPASS V 3.9
% 4.40/4.58 SPASS beiseite: Proof found.
% 4.40/4.58 % SZS status Theorem
% 4.40/4.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.40/4.58 SPASS derived 9489 clauses, backtracked 4861 clauses, performed 88 splits and kept 9156 clauses.
% 4.40/4.58 SPASS allocated 84928 KBytes.
% 4.40/4.58 SPASS spent 0:00:04.23 on the problem.
% 4.40/4.58 0:00:00.04 for the input.
% 4.40/4.58 0:00:00.00 for the FLOTTER CNF translation.
% 4.40/4.58 0:00:00.08 for inferences.
% 4.40/4.58 0:00:00.09 for the backtracking.
% 4.40/4.58 0:00:03.75 for the reduction.
% 4.40/4.58
% 4.40/4.58
% 4.40/4.58 Here is a proof with depth 5, length 281 :
% 4.40/4.58 % SZS output start Refutation
% 4.40/4.58 1[0:Inp] || -> ssList(sk1)*.
% 4.40/4.58 2[0:Inp] || -> ssList(sk2)*.
% 4.40/4.58 6[0:Inp] || -> equal(sk3,sk1)**.
% 4.40/4.58 7[0:Inp] || -> singletonP(sk3)*.
% 4.40/4.58 8[0:Inp] ssItem(u) || -> ssItem(sk5(u))*.
% 4.40/4.58 9[0:Inp] ssItem(u) || -> memberP(sk1,sk5(u))*.
% 4.40/4.58 10[0:Inp] ssItem(u) || equal(sk5(u),u)** -> .
% 4.40/4.58 11[0:Inp] || -> equalelemsP(nil)*.
% 4.40/4.58 12[0:Inp] || -> duplicatefreeP(nil)*.
% 4.40/4.58 13[0:Inp] || -> strictorderedP(nil)*.
% 4.40/4.58 14[0:Inp] || -> totalorderedP(nil)*.
% 4.40/4.58 15[0:Inp] || -> strictorderP(nil)*.
% 4.40/4.58 16[0:Inp] || -> totalorderP(nil)*.
% 4.40/4.58 17[0:Inp] || -> cyclefreeP(nil)*.
% 4.40/4.58 18[0:Inp] || -> ssList(nil)*.
% 4.40/4.58 21[0:Inp] || singletonP(nil)* -> .
% 4.40/4.58 22[0:Inp] || -> ssItem(skaf83(u))*.
% 4.40/4.58 23[0:Inp] || -> ssList(skaf82(u))*.
% 4.40/4.58 57[0:Inp] || -> ssItem(skaf44(u))*.
% 4.40/4.58 74[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 4.40/4.58 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 4.40/4.58 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 4.40/4.58 77[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 4.40/4.58 78[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 4.40/4.58 79[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 4.40/4.58 80[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 4.40/4.58 81[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 4.40/4.58 82[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 4.40/4.58 97[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf50(u),skaf49(u))*.
% 4.40/4.58 106[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 4.40/4.58 107[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 4.40/4.58 109[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 4.40/4.58 111[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 4.40/4.58 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 4.40/4.58 171[0:Inp] ssItem(u) ssItem(v) ssList(w) || memberP(cons(v,w),u)* -> equal(u,v) memberP(w,u).
% 4.40/4.58 173[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 4.40/4.58 174[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 4.40/4.58 175[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 4.40/4.58 176[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 4.40/4.58 187[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).
% 4.40/4.58 196[0:Rew:6.0,7.0] || -> singletonP(sk1)*.
% 4.40/4.58 284[0:Res:2.0,82.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 4.40/4.58 390[0:Res:1.0,176.0] || -> totalorderP(sk1) equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 4.40/4.58 391[0:Res:1.0,175.0] || -> strictorderP(sk1) equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 4.40/4.58 392[0:Res:1.0,174.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.40/4.58 393[0:Res:1.0,173.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.40/4.58 432[0:Res:1.0,119.0] || -> equal(nil,sk1) equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 4.40/4.58 434[0:Res:1.0,111.1] singletonP(sk1) || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 4.40/4.58 449[0:Res:1.0,97.0] || -> cyclefreeP(sk1) leq(skaf50(sk1),skaf49(sk1))*.
% 4.40/4.58 455[0:Res:1.0,82.0] || -> ssItem(u)* duplicatefreeP(sk1)*.
% 4.40/4.58 470[0:Res:1.0,187.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 4.40/4.58 508[0:Res:1.0,109.1] ssItem(u) || equal(cons(u,sk1),sk1)** -> .
% 4.40/4.58 545[0:MRR:434.0,196.0] || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 4.40/4.58 550[1:Spt:82.1] || -> ssItem(u)*.
% 4.40/4.58 555[1:MRR:81.0,550.0] || memberP(nil,u)* -> .
% 4.40/4.58 556[1:MRR:80.0,550.0] || -> cyclefreeP(cons(u,nil))*.
% 4.40/4.58 557[1:MRR:79.0,550.0] || -> totalorderP(cons(u,nil))*.
% 4.40/4.58 558[1:MRR:78.0,550.0] || -> strictorderP(cons(u,nil))*.
% 4.40/4.58 559[1:MRR:77.0,550.0] || -> totalorderedP(cons(u,nil))*.
% 4.40/4.58 560[1:MRR:76.0,550.0] || -> strictorderedP(cons(u,nil))*.
% 4.40/4.58 561[1:MRR:75.0,550.0] || -> duplicatefreeP(cons(u,nil))*.
% 4.40/4.58 562[1:MRR:74.0,550.0] || -> equalelemsP(cons(u,nil))*.
% 4.40/4.58 564[1:MRR:9.0,550.0] || -> memberP(sk1,sk5(u))*.
% 4.40/4.58 565[1:MRR:10.0,550.0] || equal(sk5(u),u)** -> .
% 4.40/4.58 566[1:MRR:508.0,550.0] || equal(cons(u,sk1),sk1)** -> .
% 4.40/4.58 653[1:MRR:171.1,171.0,550.0] ssList(u) || memberP(cons(v,u),w)* -> equal(w,v) memberP(u,w).
% 4.40/4.58 679[1:MRR:107.1,550.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 4.40/4.58 1306[2:Spt:470.5] || -> equal(nil,sk1)**.
% 4.40/4.58 1344[2:Rew:1306.0,545.0] || -> equal(cons(skaf44(sk1),sk1),sk1)**.
% 4.40/4.58 1415[2:MRR:1344.0,566.0] || -> .
% 4.40/4.58 1476[2:Spt:1415.0,470.5,1306.0] || equal(nil,sk1)** -> .
% 4.40/4.58 1477[2:Spt:1415.0,470.0,470.1,470.2,470.3,470.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 4.40/4.58 1482[2:MRR:432.0,1476.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 4.40/4.58 1507[3:Spt:393.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 1510[4:Spt:392.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 1516[5:Spt:449.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 1520[6:Spt:391.0] || -> strictorderP(sk1)*.
% 4.40/4.58 1521[7:Spt:390.0] || -> totalorderP(sk1)*.
% 4.40/4.58 1526[1:SpR:545.0,556.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 1527[1:SpR:545.0,557.0] || -> totalorderP(sk1)*.
% 4.40/4.58 1528[1:SpR:545.0,558.0] || -> strictorderP(sk1)*.
% 4.40/4.58 1529[1:SpR:545.0,559.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 1530[1:SpR:545.0,560.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 1531[1:SpR:545.0,561.0] || -> duplicatefreeP(sk1)*.
% 4.40/4.58 1532[1:SpR:545.0,562.0] || -> equalelemsP(sk1)*.
% 4.40/4.58 1607[1:SpR:545.0,679.1] ssList(nil) || -> equal(hd(sk1),skaf44(sk1))**.
% 4.40/4.58 1610[2:SpR:1482.0,679.1] ssList(skaf82(sk1)) || -> equal(hd(sk1),skaf83(sk1))**.
% 4.40/4.58 1614[1:SSi:1607.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || -> equal(hd(sk1),skaf44(sk1))**.
% 4.40/4.58 1637[2:Rew:1614.0,1610.1] ssList(skaf82(sk1)) || -> equal(skaf44(sk1),skaf83(sk1))**.
% 4.40/4.58 1638[7:SSi:1637.0,23.0,196.0,1.0,1507.0,1510.0,1516.0,1520.0,1521.0,1531.0,1532.0] || -> equal(skaf44(sk1),skaf83(sk1))**.
% 4.40/4.58 1639[7:Rew:1638.0,545.0] || -> equal(cons(skaf83(sk1),nil),sk1)**.
% 4.40/4.58 2448[7:SpL:1639.0,653.1] ssList(nil) || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 2459[7:SSi:2448.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 2460[7:MRR:2459.2,555.0] || memberP(sk1,u)* -> equal(u,skaf83(sk1)).
% 4.40/4.58 2471[7:Res:564.0,2460.0] || -> equal(sk5(u),skaf83(sk1))*.
% 4.40/4.58 2473[7:UnC:2471.0,565.0] || -> .
% 4.40/4.58 2474[7:Spt:2473.0,390.0,1521.0] || totalorderP(sk1)* -> .
% 4.40/4.58 2475[7:Spt:2473.0,390.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 4.40/4.58 2476[7:MRR:2474.0,1527.0] || -> .
% 4.40/4.58 2503[6:Spt:2476.0,391.0,1520.0] || strictorderP(sk1)* -> .
% 4.40/4.58 2504[6:Spt:2476.0,391.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 4.40/4.58 2505[6:MRR:2503.0,1528.0] || -> .
% 4.40/4.58 2533[5:Spt:2505.0,449.0,1516.0] || cyclefreeP(sk1)* -> .
% 4.40/4.58 2534[5:Spt:2505.0,449.1] || -> leq(skaf50(sk1),skaf49(sk1))*.
% 4.40/4.58 2535[5:MRR:2533.0,1526.0] || -> .
% 4.40/4.58 2599[4:Spt:2535.0,392.0,1510.0] || totalorderedP(sk1)* -> .
% 4.40/4.58 2600[4:Spt:2535.0,392.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.40/4.58 2601[4:MRR:2599.0,1529.0] || -> .
% 4.40/4.58 2669[3:Spt:2601.0,393.0,1507.0] || strictorderedP(sk1)* -> .
% 4.40/4.58 2670[3:Spt:2601.0,393.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.40/4.58 2671[3:MRR:2669.0,1530.0] || -> .
% 4.40/4.58 2708[1:Spt:2671.0,82.0,82.2] ssList(u) || -> duplicatefreeP(u)*.
% 4.40/4.58 2753[2:Spt:455.0] || -> ssItem(u)*.
% 4.40/4.58 2756[2:MRR:9.0,2753.0] || -> memberP(sk1,sk5(u))*.
% 4.40/4.58 2758[2:MRR:74.0,2753.0] || -> equalelemsP(cons(u,nil))*.
% 4.40/4.58 2759[2:MRR:75.0,2753.0] || -> duplicatefreeP(cons(u,nil))*.
% 4.40/4.58 2760[2:MRR:76.0,2753.0] || -> strictorderedP(cons(u,nil))*.
% 4.40/4.58 2761[2:MRR:77.0,2753.0] || -> totalorderedP(cons(u,nil))*.
% 4.40/4.58 2762[2:MRR:78.0,2753.0] || -> strictorderP(cons(u,nil))*.
% 4.40/4.58 2763[2:MRR:79.0,2753.0] || -> totalorderP(cons(u,nil))*.
% 4.40/4.58 2764[2:MRR:80.0,2753.0] || -> cyclefreeP(cons(u,nil))*.
% 4.40/4.58 2765[2:MRR:81.0,2753.0] || memberP(nil,u)* -> .
% 4.40/4.58 2768[2:MRR:10.0,2753.0] || equal(sk5(u),u)** -> .
% 4.40/4.58 2776[2:MRR:508.0,2753.0] || equal(cons(u,sk1),sk1)** -> .
% 4.40/4.58 2856[2:MRR:171.1,171.0,2753.0] ssList(u) || memberP(cons(v,u),w)* -> equal(w,v) memberP(u,w).
% 4.40/4.58 2880[2:MRR:106.1,2753.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 4.40/4.58 3544[3:Spt:470.5] || -> equal(nil,sk1)**.
% 4.40/4.58 3582[3:Rew:3544.0,545.0] || -> equal(cons(skaf44(sk1),sk1),sk1)**.
% 4.40/4.58 3660[3:MRR:3582.0,2776.0] || -> .
% 4.40/4.58 3727[3:Spt:3660.0,470.5,3544.0] || equal(nil,sk1)** -> .
% 4.40/4.58 3728[3:Spt:3660.0,470.0,470.1,470.2,470.3,470.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 4.40/4.58 3735[3:MRR:432.0,3727.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 4.40/4.58 3763[4:Spt:393.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 3766[5:Spt:392.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 3772[6:Spt:449.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 3776[7:Spt:391.0] || -> strictorderP(sk1)*.
% 4.40/4.58 3777[8:Spt:390.0] || -> totalorderP(sk1)*.
% 4.40/4.58 3786[2:SpR:545.0,2758.0] || -> equalelemsP(sk1)*.
% 4.40/4.58 3787[2:SpR:545.0,2759.0] || -> duplicatefreeP(sk1)*.
% 4.40/4.58 3788[2:SpR:545.0,2760.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 3789[2:SpR:545.0,2761.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 3790[2:SpR:545.0,2762.0] || -> strictorderP(sk1)*.
% 4.40/4.58 3791[2:SpR:545.0,2763.0] || -> totalorderP(sk1)*.
% 4.40/4.58 3792[2:SpR:545.0,2764.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 3864[2:SpR:545.0,2880.1] ssList(nil) || -> equal(tl(sk1),nil)**.
% 4.40/4.58 3867[3:SpR:3735.0,2880.1] ssList(skaf82(sk1)) || -> equal(tl(sk1),skaf82(sk1))**.
% 4.40/4.58 3870[2:SSi:3864.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || -> equal(tl(sk1),nil)**.
% 4.40/4.58 3885[3:Rew:3870.0,3867.1] ssList(skaf82(sk1)) || -> equal(skaf82(sk1),nil)**.
% 4.40/4.58 3886[8:SSi:3885.0,23.0,196.0,1.0,3763.0,3766.0,3772.0,3776.0,3777.0,3786.0,3787.0] || -> equal(skaf82(sk1),nil)**.
% 4.40/4.58 3887[8:Rew:3886.0,3735.0] || -> equal(cons(skaf83(sk1),nil),sk1)**.
% 4.40/4.58 4789[8:SpL:3887.0,2856.1] ssList(nil) || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 4801[8:SSi:4789.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 4802[8:MRR:4801.2,2765.0] || memberP(sk1,u)* -> equal(u,skaf83(sk1)).
% 4.40/4.58 4813[8:Res:2756.0,4802.0] || -> equal(sk5(u),skaf83(sk1))*.
% 4.40/4.58 4815[8:UnC:4813.0,2768.0] || -> .
% 4.40/4.58 4816[8:Spt:4815.0,390.0,3777.0] || totalorderP(sk1)* -> .
% 4.40/4.58 4817[8:Spt:4815.0,390.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 4.40/4.58 4818[8:MRR:4816.0,3791.0] || -> .
% 4.40/4.58 4828[7:Spt:4818.0,391.0,3776.0] || strictorderP(sk1)* -> .
% 4.40/4.58 4829[7:Spt:4818.0,391.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 4.40/4.58 4830[7:MRR:4828.0,3790.0] || -> .
% 4.40/4.58 4836[6:Spt:4830.0,449.0,3772.0] || cyclefreeP(sk1)* -> .
% 4.40/4.58 4837[6:Spt:4830.0,449.1] || -> leq(skaf50(sk1),skaf49(sk1))*.
% 4.40/4.58 4838[6:MRR:4836.0,3792.0] || -> .
% 4.40/4.58 4881[5:Spt:4838.0,392.0,3766.0] || totalorderedP(sk1)* -> .
% 4.40/4.58 4882[5:Spt:4838.0,392.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.40/4.58 4883[5:MRR:4881.0,3789.0] || -> .
% 4.40/4.58 4930[4:Spt:4883.0,393.0,3763.0] || strictorderedP(sk1)* -> .
% 4.40/4.58 4931[4:Spt:4883.0,393.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.40/4.58 4932[4:MRR:4930.0,3788.0] || -> .
% 4.40/4.58 4946[2:Spt:4932.0,455.1] || -> duplicatefreeP(sk1)*.
% 4.40/4.58 4949[3:Spt:284.0] || -> ssItem(u)*.
% 4.40/4.58 4954[3:MRR:81.0,4949.0] || memberP(nil,u)* -> .
% 4.40/4.58 4955[3:MRR:80.0,4949.0] || -> cyclefreeP(cons(u,nil))*.
% 4.40/4.58 4956[3:MRR:79.0,4949.0] || -> totalorderP(cons(u,nil))*.
% 4.40/4.58 4957[3:MRR:78.0,4949.0] || -> strictorderP(cons(u,nil))*.
% 4.40/4.58 4958[3:MRR:77.0,4949.0] || -> totalorderedP(cons(u,nil))*.
% 4.40/4.58 4959[3:MRR:76.0,4949.0] || -> strictorderedP(cons(u,nil))*.
% 4.40/4.58 4961[3:MRR:74.0,4949.0] || -> equalelemsP(cons(u,nil))*.
% 4.40/4.58 4963[3:MRR:9.0,4949.0] || -> memberP(sk1,sk5(u))*.
% 4.40/4.58 4964[3:MRR:10.0,4949.0] || equal(sk5(u),u)** -> .
% 4.40/4.58 4965[3:MRR:508.0,4949.0] || equal(cons(u,sk1),sk1)** -> .
% 4.40/4.58 5052[3:MRR:171.1,171.0,4949.0] ssList(u) || memberP(cons(v,u),w)* -> equal(w,v) memberP(u,w).
% 4.40/4.58 5078[3:MRR:107.1,4949.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 4.40/4.58 5750[4:Spt:470.5] || -> equal(nil,sk1)**.
% 4.40/4.58 5795[4:Rew:5750.0,545.0] || -> equal(cons(skaf44(sk1),sk1),sk1)**.
% 4.40/4.58 5866[4:MRR:5795.0,4965.0] || -> .
% 4.40/4.58 5933[4:Spt:5866.0,470.5,5750.0] || equal(nil,sk1)** -> .
% 4.40/4.58 5934[4:Spt:5866.0,470.0,470.1,470.2,470.3,470.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 4.40/4.58 5941[4:MRR:432.0,5933.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 4.40/4.58 5969[5:Spt:393.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 5972[6:Spt:392.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 5978[7:Spt:449.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 5982[8:Spt:391.0] || -> strictorderP(sk1)*.
% 4.40/4.58 5983[9:Spt:390.0] || -> totalorderP(sk1)*.
% 4.40/4.58 5992[3:SpR:545.0,4955.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 5993[3:SpR:545.0,4956.0] || -> totalorderP(sk1)*.
% 4.40/4.58 5994[3:SpR:545.0,4957.0] || -> strictorderP(sk1)*.
% 4.40/4.58 5995[3:SpR:545.0,4958.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 5996[3:SpR:545.0,4959.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 5998[3:SpR:545.0,4961.0] || -> equalelemsP(sk1)*.
% 4.40/4.58 6078[3:SpR:545.0,5078.1] ssList(nil) || -> equal(hd(sk1),skaf44(sk1))**.
% 4.40/4.58 6081[4:SpR:5941.0,5078.1] ssList(skaf82(sk1)) || -> equal(hd(sk1),skaf83(sk1))**.
% 4.40/4.58 6085[3:SSi:6078.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || -> equal(hd(sk1),skaf44(sk1))**.
% 4.40/4.58 6108[4:Rew:6085.0,6081.1] ssList(skaf82(sk1)) || -> equal(skaf44(sk1),skaf83(sk1))**.
% 4.40/4.58 6109[9:SSi:6108.0,23.0,196.0,1.0,4946.0,5969.0,5972.0,5978.0,5982.0,5983.0,5998.0] || -> equal(skaf44(sk1),skaf83(sk1))**.
% 4.40/4.58 6110[9:Rew:6109.0,545.0] || -> equal(cons(skaf83(sk1),nil),sk1)**.
% 4.40/4.58 7034[9:SpL:6110.0,5052.1] ssList(nil) || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 7045[9:SSi:7034.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.40/4.58 7046[9:MRR:7045.2,4954.0] || memberP(sk1,u)* -> equal(u,skaf83(sk1)).
% 4.40/4.58 7057[9:Res:4963.0,7046.0] || -> equal(sk5(u),skaf83(sk1))*.
% 4.40/4.58 7059[9:UnC:7057.0,4964.0] || -> .
% 4.40/4.58 7060[9:Spt:7059.0,390.0,5983.0] || totalorderP(sk1)* -> .
% 4.40/4.58 7061[9:Spt:7059.0,390.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 4.40/4.58 7062[9:MRR:7060.0,5993.0] || -> .
% 4.40/4.58 7092[8:Spt:7062.0,391.0,5982.0] || strictorderP(sk1)* -> .
% 4.40/4.58 7093[8:Spt:7062.0,391.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 4.40/4.58 7094[8:MRR:7092.0,5994.0] || -> .
% 4.40/4.58 7123[7:Spt:7094.0,449.0,5978.0] || cyclefreeP(sk1)* -> .
% 4.40/4.58 7124[7:Spt:7094.0,449.1] || -> leq(skaf50(sk1),skaf49(sk1))*.
% 4.40/4.58 7125[7:MRR:7123.0,5992.0] || -> .
% 4.40/4.58 7191[6:Spt:7125.0,392.0,5972.0] || totalorderedP(sk1)* -> .
% 4.40/4.58 7192[6:Spt:7125.0,392.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.40/4.58 7193[6:MRR:7191.0,5995.0] || -> .
% 4.40/4.58 7263[5:Spt:7193.0,393.0,5969.0] || strictorderedP(sk1)* -> .
% 4.40/4.58 7264[5:Spt:7193.0,393.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.40/4.58 7265[5:MRR:7263.0,5996.0] || -> .
% 4.40/4.58 7303[3:Spt:7265.0,284.1] || -> duplicatefreeP(sk2)*.
% 4.40/4.58 8349[4:Spt:470.5] || -> equal(nil,sk1)**.
% 4.40/4.58 8365[4:Rew:8349.0,21.0] || singletonP(sk1)* -> .
% 4.40/4.58 8448[4:MRR:8365.0,196.0] || -> .
% 4.40/4.58 8533[4:Spt:8448.0,470.5,8349.0] || equal(nil,sk1)** -> .
% 4.40/4.58 8534[4:Spt:8448.0,470.0,470.1,470.2,470.3,470.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 4.40/4.58 8542[4:MRR:432.0,8533.0] || -> equal(cons(skaf83(sk1),skaf82(sk1)),sk1)**.
% 4.40/4.58 8566[5:Spt:393.0] || -> strictorderedP(sk1)*.
% 4.40/4.58 8569[6:Spt:392.0] || -> totalorderedP(sk1)*.
% 4.40/4.58 8575[7:Spt:449.0] || -> cyclefreeP(sk1)*.
% 4.40/4.58 8579[8:Spt:391.0] || -> strictorderP(sk1)*.
% 4.40/4.58 8580[9:Spt:390.0] || -> totalorderP(sk1)*.
% 4.40/4.58 8589[0:SpR:545.0,74.1] ssItem(skaf44(sk1)) || -> equalelemsP(sk1)*.
% 4.40/4.58 8592[9:SSi:8589.0,57.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0] || -> equalelemsP(sk1)*.
% 4.40/4.58 8605[0:SpR:545.0,76.1] ssItem(skaf44(sk1)) || -> strictorderedP(sk1)*.
% 4.40/4.58 8606[0:SpR:545.0,77.1] ssItem(skaf44(sk1)) || -> totalorderedP(sk1)*.
% 4.40/4.58 8607[0:SpR:545.0,78.1] ssItem(skaf44(sk1)) || -> strictorderP(sk1)*.
% 4.71/4.95 8608[0:SpR:545.0,79.1] ssItem(skaf44(sk1)) || -> totalorderP(sk1)*.
% 4.71/4.95 8609[0:SpR:545.0,80.1] ssItem(skaf44(sk1)) || -> cyclefreeP(sk1)*.
% 4.71/4.95 8769[0:SpR:545.0,106.2] ssList(nil) ssItem(skaf44(sk1)) || -> equal(tl(sk1),nil)**.
% 4.71/4.95 8773[4:SpR:8542.0,106.2] ssList(skaf82(sk1)) ssItem(skaf83(sk1)) || -> equal(tl(sk1),skaf82(sk1))**.
% 4.71/4.95 8776[9:SSi:8769.1,8769.0,57.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0,8592.0,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0] || -> equal(tl(sk1),nil)**.
% 4.71/4.95 8795[9:Rew:8776.0,8773.2] ssList(skaf82(sk1)) ssItem(skaf83(sk1)) || -> equal(skaf82(sk1),nil)**.
% 4.71/4.95 8796[9:SSi:8795.1,8795.0,22.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0,8592.0,23.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0,8592.0] || -> equal(skaf82(sk1),nil)**.
% 4.71/4.95 8797[9:Rew:8796.0,8542.0] || -> equal(cons(skaf83(sk1),nil),sk1)**.
% 4.71/4.95 13195[9:SpL:8797.0,171.3] ssItem(u) ssItem(skaf83(sk1)) ssList(nil) || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.71/4.95 13207[9:SSi:13195.2,13195.1,18.0,17.0,16.0,15.0,14.0,13.0,12.0,11.0,22.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0,8592.0] ssItem(u) || memberP(sk1,u) -> equal(u,skaf83(sk1)) memberP(nil,u)*.
% 4.71/4.95 13208[9:MRR:13207.3,81.1] ssItem(u) || memberP(sk1,u)* -> equal(u,skaf83(sk1)).
% 4.71/4.95 13224[9:Res:9.1,13208.1] ssItem(u) ssItem(sk5(u)) || -> equal(sk5(u),skaf83(sk1))*.
% 4.71/4.95 13226[9:SSi:13224.1,8.1] ssItem(u) || -> equal(sk5(u),skaf83(sk1))*.
% 4.71/4.95 13245[9:SpL:13226.1,10.1] ssItem(u) ssItem(u) || equal(skaf83(sk1),u)* -> .
% 4.71/4.95 13251[9:Obv:13245.0] ssItem(u) || equal(skaf83(sk1),u)* -> .
% 4.71/4.95 13332[9:EqR:13251.1] ssItem(skaf83(sk1)) || -> .
% 4.71/4.95 13336[9:SSi:13332.0,22.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0,8580.0,8592.0] || -> .
% 4.71/4.95 13338[9:Spt:13336.0,390.0,8580.0] || totalorderP(sk1)* -> .
% 4.71/4.95 13339[9:Spt:13336.0,390.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 4.71/4.95 13341[8:SSi:8608.0,57.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0,8579.0] || -> totalorderP(sk1)*.
% 4.71/4.95 13342[9:MRR:13341.0,13338.0] || -> .
% 4.71/4.95 13436[8:Spt:13342.0,391.0,8579.0] || strictorderP(sk1)* -> .
% 4.71/4.95 13437[8:Spt:13342.0,391.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 4.71/4.95 13439[7:SSi:8607.0,57.0,196.0,1.0,4946.0,8566.0,8569.0,8575.0] || -> strictorderP(sk1)*.
% 4.71/4.95 13440[8:MRR:13439.0,13436.0] || -> .
% 4.71/4.95 13488[7:Spt:13440.0,449.0,8575.0] || cyclefreeP(sk1)* -> .
% 4.71/4.95 13489[7:Spt:13440.0,449.1] || -> leq(skaf50(sk1),skaf49(sk1))*.
% 4.71/4.95 13491[6:SSi:8609.0,57.0,196.0,1.0,4946.0,8566.0,8569.0] || -> cyclefreeP(sk1)*.
% 4.71/4.95 13492[7:MRR:13491.0,13488.0] || -> .
% 4.71/4.95 13573[6:Spt:13492.0,392.0,8569.0] || totalorderedP(sk1)* -> .
% 4.71/4.95 13574[6:Spt:13492.0,392.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.71/4.95 13576[5:SSi:8606.0,57.0,196.0,1.0,4946.0,8566.0] || -> totalorderedP(sk1)*.
% 4.71/4.95 13577[6:MRR:13576.0,13573.0] || -> .
% 4.71/4.95 13671[5:Spt:13577.0,393.0,8566.0] || strictorderedP(sk1)* -> .
% 4.71/4.95 13672[5:Spt:13577.0,393.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.71/4.95 13674[2:SSi:8605.0,57.0,196.0,1.0,4946.0] || -> strictorderedP(sk1)*.
% 4.71/4.95 13675[5:MRR:13674.0,13671.0] || -> .
% 4.71/4.95 % SZS output end Refutation
% 4.71/4.95 Formulae used in the proof : co1_1 co1_2 co1_6 co1_7 co1_8 co1_9 co1_10 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause11 clause12 clause13 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause87 clause96 clause97 clause99 clause101 clause109 clause161 clause163 clause164 clause165 clause166 clause177
% 4.71/4.95
%------------------------------------------------------------------------------