TSTP Solution File: LAT387+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Sun Jul 17 06:51:50 EDT 2022
% Result : Theorem 5.50s 5.67s
% Output : Refutation 6.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 29 11:47:59 EDT 2022
% 0.11/0.33 % CPUTime :
% 5.50/5.67
% 5.50/5.67 SPASS V 3.9
% 5.50/5.67 SPASS beiseite: Proof found.
% 5.50/5.67 % SZS status Theorem
% 5.50/5.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.50/5.67 SPASS derived 16222 clauses, backtracked 5058 clauses, performed 102 splits and kept 8996 clauses.
% 5.50/5.67 SPASS allocated 114390 KBytes.
% 5.50/5.67 SPASS spent 0:00:05.32 on the problem.
% 5.50/5.67 0:00:00.04 for the input.
% 5.50/5.67 0:00:00.12 for the FLOTTER CNF translation.
% 5.50/5.67 0:00:00.20 for inferences.
% 5.50/5.67 0:00:00.22 for the backtracking.
% 5.50/5.67 0:00:04.64 for the reduction.
% 5.50/5.67
% 5.50/5.67
% 5.50/5.67 Here is a proof with depth 9, length 301 :
% 5.50/5.67 % SZS output start Refutation
% 5.50/5.67 1[0:Inp] || -> aSet0(xU)*.
% 5.50/5.67 2[0:Inp] || -> aCompleteLattice0(xU)*.
% 5.50/5.67 3[0:Inp] || -> aFunction0(xf)*.
% 5.50/5.67 4[0:Inp] || -> isMonotone0(xf)*.
% 5.50/5.67 5[0:Inp] || -> aSet0(xS)*.
% 5.50/5.67 6[0:Inp] || -> aSet0(xT)*.
% 5.50/5.67 7[0:Inp] || -> aSet0(xP)*.
% 5.50/5.67 10[0:Inp] || -> aElementOf0(xp,xU)*.
% 5.50/5.67 11[0:Inp] || -> SkC1 aElementOf0(skc3,xT)*.
% 5.50/5.67 13[0:Inp] || -> aElementOf0(skf32(u),xU)*.
% 5.50/5.67 14[0:Inp] || -> equal(szRzazndt0(xf),xU)**.
% 5.50/5.67 18[0:Inp] || aFixedPointOf0(xp,xf)* -> SkC0.
% 5.50/5.67 19[0:Inp] || sdtlseqdt0(skc3,xp)* -> SkC1.
% 5.50/5.67 21[0:Inp] || -> equal(szRzazndt0(xf),szDzozmdt0(xf))**.
% 5.50/5.67 23[0:Inp] aElement0(u) || -> sdtlseqdt0(u,u)*.
% 5.50/5.67 24[0:Inp] aFunction0(u) || -> aSet0(szDzozmdt0(u))*.
% 5.50/5.67 28[0:Inp] || -> aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)*.
% 5.50/5.67 29[0:Inp] || -> aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU)*.
% 5.50/5.67 30[0:Inp] || SkC0 SkC1 -> aElementOf0(skc2,xS)*.
% 5.50/5.67 32[0:Inp] || aElementOf0(u,xS) -> aFixedPointOf0(u,xf)*.
% 5.50/5.67 34[0:Inp] || aElementOf0(u,xT)* -> aElementOf0(u,xS).
% 5.50/5.67 35[0:Inp] || aElementOf0(u,xP)* -> aElementOf0(u,xU).
% 5.50/5.67 36[0:Inp] || aElementOf0(u,xP) -> sdtlseqdt0(xp,u)*.
% 5.50/5.67 38[0:Inp] || SkC0 SkC1 sdtlseqdt0(xp,skc2)* -> .
% 5.50/5.67 43[0:Inp] || aElementOf0(u,xS) -> aElementOf0(u,szDzozmdt0(xf))*.
% 5.50/5.67 45[0:Inp] || aLowerBoundOfIn0(u,xP,xU)* -> sdtlseqdt0(u,xp).
% 5.50/5.67 46[0:Inp] aSet0(u) || aElementOf0(v,u)* -> aElement0(v).
% 5.50/5.67 47[0:Inp] aSet0(u) || -> isEmpty0(u) aElementOf0(skf19(u),u)*.
% 5.50/5.67 50[0:Inp] aSet0(u) || -> SkP0(u) aElementOf0(skf36(u),u)*.
% 5.50/5.67 51[0:Inp] || aElementOf0(u,xS) -> equal(sdtlpdtrp0(xf,u),u)**.
% 5.50/5.67 53[0:Inp] || aElementOf0(u,xP) -> sdtlseqdt0(sdtlpdtrp0(xf,xp),u)*.
% 5.50/5.67 59[0:Inp] aSet0(u) || aElementOf0(skf36(v),xU)*+ -> SkP0(u)*.
% 5.50/5.67 60[0:Inp] || SkC0 SkC1 aElementOf0(u,xT) -> sdtlseqdt0(u,skc2)*.
% 5.50/5.67 61[0:Inp] aFunction0(u) || aFixedPointOf0(v,u) -> aElementOf0(v,szDzozmdt0(u))*.
% 5.50/5.67 62[0:Inp] SkP0(u) || aElementOf0(v,u) -> sdtlseqdt0(skf32(u),v)*.
% 5.50/5.67 64[0:Inp] || aElementOf0(u,xP) aElementOf0(v,xT) -> sdtlseqdt0(v,u)*.
% 5.50/5.67 65[0:Inp] || aElementOf0(u,xU)+ -> sdtlseqdt0(u,xp)* aElementOf0(skf38(v),xP)*.
% 5.50/5.67 66[0:Inp] || aElementOf0(xp,szDzozmdt0(xf))* equal(sdtlpdtrp0(xf,xp),xp) -> SkC0.
% 5.50/5.67 73[0:Inp] aSet0(u) || aElementOf0(v,w)*+ aSubsetOf0(w,u)* -> aElementOf0(v,u)*.
% 5.50/5.67 74[0:Inp] aSet0(u) aSet0(v) || -> aSubsetOf0(v,u)* aElementOf0(skf20(v,w),v)*.
% 5.50/5.67 76[0:Inp] aFunction0(u) || aElementOf0(v,szDzozmdt0(u)) -> aElementOf0(sdtlpdtrp0(u,v),szRzazndt0(u))*.
% 5.50/5.67 78[0:Inp] aSet0(u) aSet0(v) || aElementOf0(skf20(v,u),u)* -> aSubsetOf0(v,u).
% 5.50/5.67 79[0:Inp] aSet0(u) || aSubsetOf0(v,u) aLowerBoundOfIn0(w,v,u)* -> aElementOf0(w,u).
% 5.50/5.67 87[0:Inp] SkP0(u) || aElementOf0(v,xU) -> sdtlseqdt0(v,skf32(u)) aElementOf0(skf33(v,u),u)*.
% 5.50/5.67 89[0:Inp] aElement0(u) aElement0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 5.50/5.67 92[0:Inp] SkP0(u) || aElementOf0(v,xU) sdtlseqdt0(v,skf33(v,w))*+ -> sdtlseqdt0(v,skf32(u))*.
% 5.50/5.67 94[0:Inp] || aElementOf0(u,xU) sdtlseqdt0(sdtlpdtrp0(xf,u),u)*+ -> aElementOf0(u,xP) aElementOf0(skf37(v),xT)*.
% 5.50/5.67 95[0:Inp] || aElementOf0(u,xU) sdtlseqdt0(skf37(u),u) sdtlseqdt0(sdtlpdtrp0(xf,u),u)* -> aElementOf0(u,xP).
% 5.50/5.67 96[0:Inp] || aElementOf0(u,xU) sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aUpperBoundOfIn0(u,xT,xU) -> aElementOf0(u,xP).
% 5.50/5.67 106[0:Inp] aElement0(u) aElement0(v) aElement0(w) || sdtlseqdt0(v,u)*+ sdtlseqdt0(w,v)* -> sdtlseqdt0(w,u)*.
% 5.50/5.67 107[0:Inp] || aElementOf0(u,szDzozmdt0(xf)) sdtlseqdt0(u,v) aElementOf0(v,szDzozmdt0(xf)) -> sdtlseqdt0(sdtlpdtrp0(xf,u),sdtlpdtrp0(xf,v))*.
% 5.50/5.67 115[0:Rew:14.0,21.0] || -> equal(szDzozmdt0(xf),xU)**.
% 5.50/5.67 116[0:Rew:115.0,43.1] || aElementOf0(u,xS)* -> aElementOf0(u,xU).
% 5.50/5.67 117[0:Rew:115.0,66.0] || aElementOf0(xp,xU) equal(sdtlpdtrp0(xf,xp),xp)** -> SkC0.
% 5.50/5.67 118[0:MRR:117.0,10.0] || equal(sdtlpdtrp0(xf,xp),xp)** -> SkC0.
% 5.50/5.67 121[0:Rew:115.0,107.2,115.0,107.0] || sdtlseqdt0(u,v) aElementOf0(v,xU) aElementOf0(u,xU) -> sdtlseqdt0(sdtlpdtrp0(xf,u),sdtlpdtrp0(xf,v))*.
% 5.50/5.67 126[1:Spt:94.0,94.1,94.2] || aElementOf0(u,xU) sdtlseqdt0(sdtlpdtrp0(xf,u),u)* -> aElementOf0(u,xP).
% 5.50/5.67 127[2:Spt:65.0,65.1] || aElementOf0(u,xU) -> sdtlseqdt0(u,xp)*.
% 5.50/5.67 130[3:Spt:60.1] || SkC1* -> .
% 5.50/5.67 131[3:MRR:11.0,130.0] || -> aElementOf0(skc3,xT)*.
% 5.50/5.67 132[3:MRR:19.1,130.0] || sdtlseqdt0(skc3,xp)* -> .
% 5.50/5.67 139[3:Res:127.1,132.0] || aElementOf0(skc3,xU)* -> .
% 5.50/5.67 144[3:Res:131.0,34.0] || -> aElementOf0(skc3,xS)*.
% 5.50/5.67 145[3:Res:144.0,116.0] || -> aElementOf0(skc3,xU)*.
% 5.50/5.67 146[3:MRR:145.0,139.0] || -> .
% 5.50/5.67 147[3:Spt:146.0,60.1,130.0] || -> SkC1*.
% 5.50/5.67 148[3:Spt:146.0,60.0,60.2,60.3] || SkC0 aElementOf0(u,xT) -> sdtlseqdt0(u,skc2)*.
% 5.50/5.67 149[3:MRR:30.1,147.0] || SkC0 -> aElementOf0(skc2,xS)*.
% 5.50/5.67 150[3:MRR:38.1,147.0] || SkC0 sdtlseqdt0(xp,skc2)* -> .
% 5.50/5.67 153[4:Spt:18.1] || -> SkC0*.
% 5.50/5.67 156[4:MRR:149.0,153.0] || -> aElementOf0(skc2,xS)*.
% 5.50/5.67 157[4:MRR:150.0,153.0] || sdtlseqdt0(xp,skc2)* -> .
% 5.50/5.67 160[4:Res:156.0,116.0] || -> aElementOf0(skc2,xU)*.
% 5.50/5.67 162[4:Res:36.1,157.0] || aElementOf0(skc2,xP)* -> .
% 5.50/5.67 167[0:Res:28.0,45.0] || -> sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)*.
% 5.50/5.67 168[1:Res:167.0,126.1] || aElementOf0(xp,xU) -> aElementOf0(xp,xP)*.
% 5.50/5.67 169[1:MRR:168.0,10.0] || -> aElementOf0(xp,xP)*.
% 5.50/5.67 180[1:SpL:51.1,126.1] || aElementOf0(u,xS) aElementOf0(u,xU) sdtlseqdt0(u,u)* -> aElementOf0(u,xP).
% 5.50/5.67 183[1:MRR:180.1,116.1] || aElementOf0(u,xS) sdtlseqdt0(u,u)* -> aElementOf0(u,xP).
% 5.50/5.67 189[0:Res:47.2,34.0] aSet0(xT) || -> isEmpty0(xT) aElementOf0(skf19(xT),xS)*.
% 5.50/5.67 192[0:SSi:189.0,6.0] || -> isEmpty0(xT) aElementOf0(skf19(xT),xS)*.
% 5.50/5.67 194[0:Res:50.2,35.0] aSet0(xP) || -> SkP0(xP) aElementOf0(skf36(xP),xU)*.
% 5.50/5.67 195[0:Res:50.2,116.0] aSet0(xS) || -> SkP0(xS) aElementOf0(skf36(xS),xU)*.
% 5.50/5.67 196[0:Res:50.2,34.0] aSet0(xT) || -> SkP0(xT) aElementOf0(skf36(xT),xS)*.
% 5.50/5.67 197[0:SSi:194.0,7.0] || -> SkP0(xP) aElementOf0(skf36(xP),xU)*.
% 5.50/5.67 198[0:SSi:195.0,5.0] || -> SkP0(xS) aElementOf0(skf36(xS),xU)*.
% 5.50/5.67 199[0:SSi:196.0,6.0] || -> SkP0(xT) aElementOf0(skf36(xT),xS)*.
% 5.50/5.67 200[0:Res:199.1,116.0] || -> SkP0(xT) aElementOf0(skf36(xT),xU)*.
% 5.50/5.67 201[0:Res:10.0,46.1] aSet0(xU) || -> aElement0(xp)*.
% 5.50/5.67 202[0:Res:13.0,46.1] aSet0(xU) || -> aElement0(skf32(u))*.
% 5.50/5.67 204[4:Res:160.0,46.1] aSet0(xU) || -> aElement0(skc2)*.
% 5.50/5.67 207[0:Res:197.1,46.1] aSet0(xU) || -> SkP0(xP) aElement0(skf36(xP))*.
% 5.50/5.67 208[0:Res:198.1,46.1] aSet0(xU) || -> SkP0(xS) aElement0(skf36(xS))*.
% 5.50/5.67 212[0:Res:192.1,46.1] aSet0(xS) || -> isEmpty0(xT) aElement0(skf19(xT))*.
% 5.50/5.67 215[0:Res:199.1,46.1] aSet0(xS) || -> SkP0(xT) aElement0(skf36(xT))*.
% 5.50/5.67 217[0:SSi:201.0,2.0,1.0] || -> aElement0(xp)*.
% 5.50/5.67 218[4:SSi:204.0,2.0,1.0] || -> aElement0(skc2)*.
% 5.50/5.67 219[0:SSi:202.0,2.0,1.0] || -> aElement0(skf32(u))*.
% 5.50/5.67 223[0:SSi:207.0,2.0,1.0] || -> SkP0(xP) aElement0(skf36(xP))*.
% 5.50/5.67 224[0:SSi:208.0,2.0,1.0] || -> SkP0(xS) aElement0(skf36(xS))*.
% 5.50/5.67 225[0:SSi:212.0,5.0] || -> isEmpty0(xT) aElement0(skf19(xT))*.
% 5.50/5.67 226[0:SSi:215.0,5.0] || -> SkP0(xT) aElement0(skf36(xT))*.
% 5.50/5.67 234[0:Res:198.1,59.1] aSet0(u) || -> SkP0(xS)* SkP0(u)*.
% 5.50/5.67 235[0:Res:50.2,59.1] aSet0(xU) aSet0(u) || -> SkP0(xU)* SkP0(u)*.
% 5.50/5.67 236[0:Res:200.1,59.1] aSet0(u) || -> SkP0(xT)* SkP0(u)*.
% 5.50/5.67 237[0:Con:235.1] aSet0(xU) || -> SkP0(xU)*.
% 5.50/5.67 238[0:SSi:237.0,2.0,1.0] || -> SkP0(xU)*.
% 5.50/5.67 279[1:Res:23.1,183.1] aElement0(u) || aElementOf0(u,xS) -> aElementOf0(u,xP)*.
% 5.50/5.67 292[4:Res:279.2,162.0] aElement0(skc2) || aElementOf0(skc2,xS)* -> .
% 5.50/5.67 295[4:SSi:292.0,218.0] || aElementOf0(skc2,xS)* -> .
% 5.50/5.67 296[4:MRR:295.0,156.0] || -> .
% 5.50/5.67 297[4:Spt:296.0,18.1,153.0] || SkC0* -> .
% 5.50/5.67 298[4:Spt:296.0,18.0] || aFixedPointOf0(xp,xf)* -> .
% 5.50/5.67 302[4:MRR:118.1,297.0] || equal(sdtlpdtrp0(xf,xp),xp)** -> .
% 5.50/5.67 303[4:Res:32.1,298.0] || aElementOf0(xp,xS)* -> .
% 5.50/5.67 310[0:Res:61.2,46.1] aFunction0(u) aSet0(szDzozmdt0(u)) || aFixedPointOf0(v,u)* -> aElement0(v).
% 5.50/5.67 312[0:SSi:310.1,24.1] aFunction0(u) || aFixedPointOf0(v,u)* -> aElement0(v).
% 5.50/5.67 314[5:Spt:226.0] || -> SkP0(xT)*.
% 5.50/5.67 315[6:Spt:225.0] || -> isEmpty0(xT)*.
% 5.50/5.67 323[7:Spt:223.0] || -> SkP0(xP)*.
% 5.50/5.67 355[0:Res:32.1,312.1] aFunction0(xf) || aElementOf0(u,xS)* -> aElement0(u).
% 5.50/5.67 356[0:SSi:355.0,4.0,3.0] || aElementOf0(u,xS)* -> aElement0(u).
% 5.50/5.67 357[1:MRR:279.0,356.1] || aElementOf0(u,xS) -> aElementOf0(u,xP)*.
% 5.50/5.67 388[0:SpR:14.0,76.2] aFunction0(xf) || aElementOf0(u,szDzozmdt0(xf)) -> aElementOf0(sdtlpdtrp0(xf,u),xU)*.
% 5.50/5.67 394[0:Rew:115.0,388.1] aFunction0(xf) || aElementOf0(u,xU) -> aElementOf0(sdtlpdtrp0(xf,u),xU)*.
% 5.50/5.67 395[0:SSi:394.0,4.0,3.0] || aElementOf0(u,xU) -> aElementOf0(sdtlpdtrp0(xf,u),xU)*.
% 5.50/5.67 413[0:Res:395.1,46.1] aSet0(xU) || aElementOf0(u,xU) -> aElement0(sdtlpdtrp0(xf,u))*.
% 5.50/5.67 415[0:SSi:413.0,2.0,1.0,238.0] || aElementOf0(u,xU) -> aElement0(sdtlpdtrp0(xf,u))*.
% 5.50/5.67 422[0:Res:74.3,35.0] aSet0(u) aSet0(xP) || -> aSubsetOf0(xP,u)* aElementOf0(skf20(xP,v),xU)*.
% 5.50/5.67 429[7:SSi:422.1,7.0,323.0] aSet0(u) || -> aSubsetOf0(xP,u)* aElementOf0(skf20(xP,v),xU)*.
% 5.50/5.67 440[8:Spt:429.0,429.1] aSet0(u) || -> aSubsetOf0(xP,u)*.
% 5.50/5.67 454[1:Res:169.0,73.1] aSet0(u) || aSubsetOf0(xP,u)* -> aElementOf0(xp,u).
% 5.50/5.67 465[8:MRR:454.1,440.1] aSet0(u) || -> aElementOf0(xp,u)*.
% 5.50/5.67 475[8:Res:465.1,34.0] aSet0(xT) || -> aElementOf0(xp,xS)*.
% 5.50/5.67 481[8:SSi:475.0,6.0,314.0,315.0] || -> aElementOf0(xp,xS)*.
% 5.50/5.67 482[8:MRR:481.0,303.0] || -> .
% 5.50/5.67 487[8:Spt:482.0,429.2] || -> aElementOf0(skf20(xP,u),xU)*.
% 5.50/5.67 581[8:Res:487.0,78.2] aSet0(xU) aSet0(xP) || -> aSubsetOf0(xP,xU)*.
% 5.50/5.67 584[8:SSi:581.1,581.0,7.0,323.0,2.0,1.0,238.0] || -> aSubsetOf0(xP,xU)*.
% 5.50/5.67 706[0:Res:28.0,79.2] aSet0(xU) || aSubsetOf0(xP,xU) -> aElementOf0(sdtlpdtrp0(xf,xp),xU)*.
% 5.50/5.67 708[0:SSi:706.0,2.0,1.0,238.0] || aSubsetOf0(xP,xU) -> aElementOf0(sdtlpdtrp0(xf,xp),xU)*.
% 5.50/5.67 709[8:MRR:708.0,584.0] || -> aElementOf0(sdtlpdtrp0(xf,xp),xU)*.
% 5.50/5.67 714[8:Res:709.0,46.1] aSet0(xU) || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 5.50/5.67 716[8:SSi:714.0,2.0,1.0,238.0] || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 5.50/5.67 1025[0:Res:36.1,92.2] SkP0(u) || aElementOf0(skf33(xp,v),xP)* aElementOf0(xp,xU) -> sdtlseqdt0(xp,skf32(u))*.
% 5.50/5.67 1030[0:MRR:1025.2,10.0] SkP0(u) || aElementOf0(skf33(xp,v),xP)*+ -> sdtlseqdt0(xp,skf32(u))*.
% 5.50/5.67 1078[0:Res:53.1,89.2] aElement0(u) aElement0(sdtlpdtrp0(xf,xp)) || aElementOf0(u,xP) sdtlseqdt0(u,sdtlpdtrp0(xf,xp))* -> equal(sdtlpdtrp0(xf,xp),u).
% 5.50/5.67 1081[0:Res:36.1,89.2] aElement0(u) aElement0(xp) || aElementOf0(u,xP) sdtlseqdt0(u,xp)* -> equal(xp,u).
% 5.50/5.67 1085[2:Res:127.1,89.2] aElement0(xp) aElement0(u) || aElementOf0(u,xU) sdtlseqdt0(xp,u)* -> equal(u,xp).
% 5.50/5.67 1105[0:SSi:1081.1,217.0] aElement0(u) || aElementOf0(u,xP) sdtlseqdt0(u,xp)* -> equal(xp,u).
% 5.50/5.67 1106[2:SSi:1085.0,217.0] aElement0(u) || aElementOf0(u,xU) sdtlseqdt0(xp,u)* -> equal(u,xp).
% 5.50/5.67 1115[8:SSi:1078.1,716.0] aElement0(u) || aElementOf0(u,xP) sdtlseqdt0(u,sdtlpdtrp0(xf,xp))* -> equal(sdtlpdtrp0(xf,xp),u).
% 5.50/5.67 1155[1:Res:121.3,126.1] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xU) aElementOf0(sdtlpdtrp0(xf,u),xU) -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 5.50/5.67 1164[1:Obv:1155.2] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xU) -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 5.50/5.67 1165[1:MRR:1164.2,395.1] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 5.50/5.67 1256[0:Res:167.0,106.3] aElement0(xp) aElement0(sdtlpdtrp0(xf,xp)) aElement0(u) || sdtlseqdt0(u,sdtlpdtrp0(xf,xp))* -> sdtlseqdt0(u,xp).
% 5.50/5.67 1266[8:SSi:1256.1,1256.0,716.0,217.0] aElement0(u) || sdtlseqdt0(u,sdtlpdtrp0(xf,xp))* -> sdtlseqdt0(u,xp).
% 5.50/5.67 1306[8:Res:121.3,1266.1] aElement0(sdtlpdtrp0(xf,u)) || sdtlseqdt0(u,xp) aElementOf0(xp,xU) aElementOf0(u,xU) -> sdtlseqdt0(sdtlpdtrp0(xf,u),xp)*.
% 5.50/5.67 1315[8:MRR:1306.0,1306.1,1306.2,415.1,127.1,10.0] || aElementOf0(u,xU) -> sdtlseqdt0(sdtlpdtrp0(xf,u),xp)*.
% 5.50/5.67 1351[8:Res:1315.1,89.2] aElement0(xp) aElement0(sdtlpdtrp0(xf,u)) || aElementOf0(u,xU) sdtlseqdt0(xp,sdtlpdtrp0(xf,u))* -> equal(sdtlpdtrp0(xf,u),xp).
% 5.50/5.67 1353[8:SSi:1351.0,217.0] aElement0(sdtlpdtrp0(xf,u)) || aElementOf0(u,xU) sdtlseqdt0(xp,sdtlpdtrp0(xf,u))* -> equal(sdtlpdtrp0(xf,u),xp).
% 5.50/5.67 1354[8:MRR:1353.0,415.1] || aElementOf0(u,xU) sdtlseqdt0(xp,sdtlpdtrp0(xf,u))* -> equal(sdtlpdtrp0(xf,u),xp).
% 5.50/5.67 1876[1:Res:357.1,1030.1] SkP0(u) || aElementOf0(skf33(xp,v),xS)*+ -> sdtlseqdt0(xp,skf32(u))*.
% 5.50/5.67 3569[1:Res:87.3,1876.1] SkP0(xS) SkP0(u) || aElementOf0(xp,xU) -> sdtlseqdt0(xp,skf32(xS))* sdtlseqdt0(xp,skf32(u))*.
% 5.50/5.67 3570[1:Con:3569.1] SkP0(xS) || aElementOf0(xp,xU) -> sdtlseqdt0(xp,skf32(xS))*.
% 5.50/5.67 4028[8:Res:121.3,1115.2] aElement0(sdtlpdtrp0(xf,u)) || sdtlseqdt0(u,xp) aElementOf0(xp,xU) aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xP)* -> equal(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,u)).
% 5.50/5.67 4043[8:MRR:4028.0,4028.1,4028.2,415.1,127.1,10.0] || aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xP)* -> equal(sdtlpdtrp0(xf,xp),sdtlpdtrp0(xf,u)).
% 5.50/5.67 6185[8:Res:36.1,1354.1] || aElementOf0(sdtlpdtrp0(xf,u),xP)* aElementOf0(u,xU) -> equal(sdtlpdtrp0(xf,u),xp).
% 5.50/5.67 6194[8:Rew:6185.2,4043.2] || aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xP)* -> equal(sdtlpdtrp0(xf,xp),xp).
% 5.50/5.67 6195[8:MRR:6194.2,302.0] || aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xP)* -> .
% 5.50/5.67 6196[8:MRR:1165.2,6195.1] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) -> .
% 5.50/5.67 6263[8:Res:127.1,6196.0] || aElementOf0(sdtlpdtrp0(xf,xp),xU)* aElementOf0(xp,xU) -> .
% 5.50/5.67 6281[8:MRR:6263.0,6263.1,395.1,10.0] || -> .
% 5.50/5.67 6292[7:Spt:6281.0,223.0,323.0] || SkP0(xP)* -> .
% 5.50/5.67 6293[7:Spt:6281.0,223.1] || -> aElement0(skf36(xP))*.
% 5.50/5.67 6294[7:MRR:197.0,6292.0] || -> aElementOf0(skf36(xP),xU)*.
% 5.50/5.67 6689[7:Res:6294.0,59.1] aSet0(u) || -> SkP0(u)*.
% 5.50/5.67 6699[7:Res:6689.1,6292.0] aSet0(xP) || -> .
% 5.50/5.67 6700[7:SSi:6699.0,7.0] || -> .
% 5.50/5.67 6703[6:Spt:6700.0,225.0,315.0] || isEmpty0(xT)* -> .
% 5.50/5.67 6704[6:Spt:6700.0,225.1] || -> aElement0(skf19(xT))*.
% 5.50/5.67 6705[6:MRR:192.0,6703.0] || -> aElementOf0(skf19(xT),xS)*.
% 5.50/5.67 6712[1:MRR:3570.1,10.0] SkP0(xS) || -> sdtlseqdt0(xp,skf32(xS))*.
% 5.50/5.67 6816[7:Spt:224.0] || -> SkP0(xS)*.
% 5.50/5.67 6817[7:MRR:6712.0,6816.0] || -> sdtlseqdt0(xp,skf32(xS))*.
% 5.50/5.67 6842[7:Res:6817.0,1106.2] aElement0(skf32(xS)) || aElementOf0(skf32(xS),xU)* -> equal(skf32(xS),xp).
% 5.50/5.67 6846[7:SSi:6842.0,219.0,5.0,6816.0] || aElementOf0(skf32(xS),xU)* -> equal(skf32(xS),xp).
% 5.50/5.67 6847[7:MRR:6846.0,13.0] || -> equal(skf32(xS),xp)**.
% 5.50/5.67 6861[7:SpR:6847.0,62.2] SkP0(xS) || aElementOf0(u,xS) -> sdtlseqdt0(xp,u)*.
% 5.50/5.67 6872[7:SSi:6861.0,5.0,6816.0] || aElementOf0(u,xS) -> sdtlseqdt0(xp,u)*.
% 5.50/5.67 6908[7:Res:6872.1,1106.2] aElement0(u) || aElementOf0(u,xS)* aElementOf0(u,xU) -> equal(u,xp).
% 5.50/5.67 6916[7:MRR:6908.0,6908.2,356.1,116.1] || aElementOf0(u,xS)* -> equal(u,xp).
% 5.50/5.67 6944[7:Res:6705.0,6916.0] || -> equal(skf19(xT),xp)**.
% 5.50/5.67 6946[7:Rew:6944.0,6705.0] || -> aElementOf0(xp,xS)*.
% 5.50/5.67 6950[7:MRR:6946.0,303.0] || -> .
% 5.50/5.67 6985[7:Spt:6950.0,224.0,6816.0] || SkP0(xS)* -> .
% 5.50/5.67 6986[7:Spt:6950.0,224.1] || -> aElement0(skf36(xS))*.
% 5.50/5.67 6988[7:MRR:234.1,6985.0] aSet0(u) || -> SkP0(u)*.
% 5.50/5.67 7005[7:Res:6988.1,6985.0] aSet0(xS) || -> .
% 5.50/5.67 7006[7:SSi:7005.0,5.0] || -> .
% 5.50/5.67 7007[5:Spt:7006.0,226.0,314.0] || SkP0(xT)* -> .
% 5.50/5.67 7008[5:Spt:7006.0,226.1] || -> aElement0(skf36(xT))*.
% 5.50/5.67 7011[5:MRR:236.1,7007.0] aSet0(u) || -> SkP0(u)*.
% 5.50/5.67 7144[5:Res:7011.1,7007.0] aSet0(xT) || -> .
% 5.50/5.67 7148[5:SSi:7144.0,6.0] || -> .
% 5.50/5.67 7151[2:Spt:7148.0,65.2] || -> aElementOf0(skf38(u),xP)*.
% 5.50/5.67 7173[3:Spt:30.0] || SkC0* -> .
% 5.50/5.67 7175[3:MRR:118.1,7173.0] || equal(sdtlpdtrp0(xf,xp),xp)** -> .
% 5.50/5.67 8625[0:Res:167.0,1105.2] aElement0(sdtlpdtrp0(xf,xp)) || aElementOf0(sdtlpdtrp0(xf,xp),xP)* -> equal(sdtlpdtrp0(xf,xp),xp).
% 5.50/5.67 15969[1:Res:167.0,1165.0] || aElementOf0(xp,xU) -> aElementOf0(sdtlpdtrp0(xf,xp),xP)*.
% 5.50/5.67 16019[1:MRR:15969.0,10.0] || -> aElementOf0(sdtlpdtrp0(xf,xp),xP)*.
% 5.50/5.67 16033[3:MRR:8625.2,7175.0] aElement0(sdtlpdtrp0(xf,xp)) || aElementOf0(sdtlpdtrp0(xf,xp),xP)* -> .
% 5.50/5.67 16034[3:MRR:16033.1,16019.0] aElement0(sdtlpdtrp0(xf,xp)) || -> .
% 5.50/5.67 16442[1:Res:16019.0,46.1] aSet0(xP) || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 5.50/5.67 16449[1:SSi:16442.0,7.0] || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 5.50/5.67 16450[3:MRR:16449.0,16034.0] || -> .
% 5.50/5.67 16453[3:Spt:16450.0,30.0,7173.0] || -> SkC0*.
% 5.50/5.67 16454[3:Spt:16450.0,30.1,30.2] || SkC1 -> aElementOf0(skc2,xS)*.
% 5.50/5.67 16456[3:MRR:38.0,16453.0] || SkC1 sdtlseqdt0(xp,skc2)* -> .
% 5.50/5.67 16586[4:Spt:11.0] || -> SkC1*.
% 5.50/5.67 16587[4:MRR:16454.0,16586.0] || -> aElementOf0(skc2,xS)*.
% 5.50/5.67 16588[4:MRR:16456.0,16586.0] || sdtlseqdt0(xp,skc2)* -> .
% 5.50/5.67 16630[4:Res:36.1,16588.0] || aElementOf0(skc2,xP)* -> .
% 5.50/5.67 16650[4:Res:357.1,16630.0] || aElementOf0(skc2,xS)* -> .
% 5.50/5.67 16651[4:MRR:16650.0,16587.0] || -> .
% 5.50/5.67 16652[4:Spt:16651.0,11.0,16586.0] || SkC1* -> .
% 5.50/5.67 16653[4:Spt:16651.0,11.1] || -> aElementOf0(skc3,xT)*.
% 5.50/5.67 16654[4:MRR:19.1,16652.0] || sdtlseqdt0(skc3,xp)* -> .
% 6.14/6.34 16676[4:Res:64.2,16654.0] || aElementOf0(xp,xP) aElementOf0(skc3,xT)* -> .
% 6.14/6.34 16677[4:MRR:16676.0,16676.1,169.0,16653.0] || -> .
% 6.14/6.34 16678[1:Spt:16677.0,94.3] || -> aElementOf0(skf37(u),xT)*.
% 6.14/6.34 16699[1:Res:16678.0,34.0] || -> aElementOf0(skf37(u),xS)*.
% 6.14/6.34 16718[2:Spt:65.0,65.1] || aElementOf0(u,xU) -> sdtlseqdt0(u,xp)*.
% 6.14/6.34 16736[3:Spt:60.2,60.3] || aElementOf0(u,xT) -> sdtlseqdt0(u,skc2)*.
% 6.14/6.34 16744[4:Spt:30.0] || SkC0* -> .
% 6.14/6.34 16746[4:MRR:118.1,16744.0] || equal(sdtlpdtrp0(xf,xp),xp)** -> .
% 6.14/6.34 16748[4:MRR:8625.2,16746.0] aElement0(sdtlpdtrp0(xf,xp)) || aElementOf0(sdtlpdtrp0(xf,xp),xP)* -> .
% 6.14/6.34 16787[1:Res:16699.0,116.0] || -> aElementOf0(skf37(u),xU)*.
% 6.14/6.34 17002[0:Res:121.3,96.1] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xU) aElementOf0(sdtlpdtrp0(xf,u),xU) aUpperBoundOfIn0(sdtlpdtrp0(xf,u),xT,xU)* -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 6.14/6.34 17022[0:Obv:17002.2] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) aElementOf0(sdtlpdtrp0(xf,u),xU) aUpperBoundOfIn0(sdtlpdtrp0(xf,u),xT,xU)* -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 6.14/6.34 17023[0:MRR:17022.2,395.1] || sdtlseqdt0(sdtlpdtrp0(xf,u),u)* aElementOf0(u,xU) aUpperBoundOfIn0(sdtlpdtrp0(xf,u),xT,xU)*+ -> aElementOf0(sdtlpdtrp0(xf,u),xP).
% 6.14/6.34 17145[0:SpL:51.1,95.2] || aElementOf0(u,xS) aElementOf0(u,xU) sdtlseqdt0(skf37(u),u)* sdtlseqdt0(u,u) -> aElementOf0(u,xP).
% 6.14/6.34 17153[0:Res:167.0,95.2] || aElementOf0(xp,xU) sdtlseqdt0(skf37(xp),xp)* -> aElementOf0(xp,xP).
% 6.14/6.34 17166[0:MRR:17153.0,10.0] || sdtlseqdt0(skf37(xp),xp)* -> aElementOf0(xp,xP).
% 6.14/6.34 17167[0:MRR:17145.1,116.1] || aElementOf0(u,xS) sdtlseqdt0(skf37(u),u)* sdtlseqdt0(u,u) -> aElementOf0(u,xP).
% 6.14/6.34 17181[2:Res:16718.1,17166.0] || aElementOf0(skf37(xp),xU)* -> aElementOf0(xp,xP).
% 6.14/6.34 17182[2:MRR:17181.0,16787.0] || -> aElementOf0(xp,xP)*.
% 6.14/6.34 20977[3:Res:16736.1,17167.1] || aElementOf0(skf37(skc2),xT)* aElementOf0(skc2,xS) sdtlseqdt0(skc2,skc2) -> aElementOf0(skc2,xP).
% 6.14/6.34 20978[3:MRR:20977.0,16678.0] || aElementOf0(skc2,xS) sdtlseqdt0(skc2,skc2)* -> aElementOf0(skc2,xP).
% 6.14/6.34 20996[3:Res:23.1,20978.1] aElement0(skc2) || aElementOf0(skc2,xS) -> aElementOf0(skc2,xP)*.
% 6.14/6.34 20999[3:MRR:20996.0,356.1] || aElementOf0(skc2,xS) -> aElementOf0(skc2,xP)*.
% 6.14/6.34 22746[0:Res:29.0,17023.2] || sdtlseqdt0(sdtlpdtrp0(xf,xp),xp)* aElementOf0(xp,xU) -> aElementOf0(sdtlpdtrp0(xf,xp),xP).
% 6.14/6.34 22782[0:MRR:22746.0,22746.1,167.0,10.0] || -> aElementOf0(sdtlpdtrp0(xf,xp),xP)*.
% 6.14/6.34 22783[4:MRR:16748.1,22782.0] aElement0(sdtlpdtrp0(xf,xp)) || -> .
% 6.14/6.34 23108[0:Res:22782.0,46.1] aSet0(xP) || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 6.14/6.34 23114[0:SSi:23108.0,7.0] || -> aElement0(sdtlpdtrp0(xf,xp))*.
% 6.14/6.34 23115[4:MRR:23114.0,22783.0] || -> .
% 6.14/6.34 23118[4:Spt:23115.0,30.0,16744.0] || -> SkC0*.
% 6.14/6.34 23119[4:Spt:23115.0,30.1,30.2] || SkC1 -> aElementOf0(skc2,xS)*.
% 6.14/6.34 23121[4:MRR:38.0,23118.0] || SkC1 sdtlseqdt0(xp,skc2)* -> .
% 6.14/6.34 23123[0:MRR:8625.1,22782.0] aElement0(sdtlpdtrp0(xf,xp)) || -> equal(sdtlpdtrp0(xf,xp),xp)**.
% 6.14/6.34 23124[0:MRR:23123.0,23114.0] || -> equal(sdtlpdtrp0(xf,xp),xp)**.
% 6.14/6.34 23131[0:Rew:23124.0,22782.0] || -> aElementOf0(xp,xP)*.
% 6.14/6.34 23214[5:Spt:11.0] || -> SkC1*.
% 6.14/6.34 23215[5:MRR:23119.0,23214.0] || -> aElementOf0(skc2,xS)*.
% 6.14/6.34 23216[5:MRR:23121.0,23214.0] || sdtlseqdt0(xp,skc2)* -> .
% 6.14/6.34 23228[5:MRR:20999.0,23215.0] || -> aElementOf0(skc2,xP)*.
% 6.14/6.34 23271[5:Res:36.1,23216.0] || aElementOf0(skc2,xP)* -> .
% 6.14/6.34 23274[5:MRR:23271.0,23228.0] || -> .
% 6.14/6.34 23275[5:Spt:23274.0,11.0,23214.0] || SkC1* -> .
% 6.14/6.34 23276[5:Spt:23274.0,11.1] || -> aElementOf0(skc3,xT)*.
% 6.14/6.34 23277[5:MRR:19.1,23275.0] || sdtlseqdt0(skc3,xp)* -> .
% 6.14/6.34 23290[5:Res:64.2,23277.0] || aElementOf0(xp,xP) aElementOf0(skc3,xT)* -> .
% 6.14/6.34 23292[5:MRR:23290.0,23290.1,17182.0,23276.0] || -> .
% 6.14/6.34 23293[3:Spt:23292.0,60.0,60.1] || SkC0 SkC1* -> .
% 6.14/6.34 23294[0:Rew:23124.0,118.0] || equal(xp,xp) -> SkC0*.
% 6.14/6.34 23295[0:Obv:23294.0] || -> SkC0*.
% 6.14/6.34 23296[3:MRR:23293.0,23295.0] || SkC1* -> .
% 6.14/6.34 23298[3:MRR:11.0,23296.0] || -> aElementOf0(skc3,xT)*.
% 6.14/6.34 23299[3:MRR:19.1,23296.0] || sdtlseqdt0(skc3,xp)* -> .
% 6.14/6.34 23312[3:Res:64.2,23299.0] || aElementOf0(xp,xP) aElementOf0(skc3,xT)* -> .
% 6.14/6.34 23314[3:MRR:23312.0,23312.1,17182.0,23298.0] || -> .
% 6.14/6.34 23315[2:Spt:23314.0,65.2] || -> aElementOf0(skf38(u),xP)*.
% 6.14/6.34 23319[0:MRR:30.0,23295.0] || SkC1 -> aElementOf0(skc2,xS)*.
% 6.14/6.34 23320[0:MRR:38.0,23295.0] || SkC1 sdtlseqdt0(xp,skc2)* -> .
% 6.14/6.34 23323[0:MRR:60.0,23295.0] || SkC1 aElementOf0(u,xT) -> sdtlseqdt0(u,skc2)*.
% 6.14/6.34 23368[3:Spt:11.0] || -> SkC1*.
% 6.14/6.34 23369[3:MRR:23319.0,23368.0] || -> aElementOf0(skc2,xS)*.
% 6.14/6.34 23370[3:MRR:23320.0,23368.0] || sdtlseqdt0(xp,skc2)* -> .
% 6.14/6.34 23372[3:MRR:23323.0,23368.0] || aElementOf0(u,xT) -> sdtlseqdt0(u,skc2)*.
% 6.14/6.34 23384[3:Res:23369.0,356.0] || -> aElement0(skc2)*.
% 6.14/6.34 23395[3:Res:36.1,23370.0] || aElementOf0(skc2,xP)* -> .
% 6.14/6.34 23590[3:Res:23372.1,17167.1] || aElementOf0(skf37(skc2),xT)* aElementOf0(skc2,xS) sdtlseqdt0(skc2,skc2) -> aElementOf0(skc2,xP).
% 6.14/6.34 23598[3:MRR:23590.0,23590.1,23590.3,16678.0,23369.0,23395.0] || sdtlseqdt0(skc2,skc2)* -> .
% 6.14/6.34 23625[3:Res:23.1,23598.0] aElement0(skc2) || -> .
% 6.14/6.34 23628[3:SSi:23625.0,23384.0] || -> .
% 6.14/6.34 23629[3:Spt:23628.0,11.0,23368.0] || SkC1* -> .
% 6.14/6.34 23630[3:Spt:23628.0,11.1] || -> aElementOf0(skc3,xT)*.
% 6.14/6.34 23631[3:MRR:19.1,23629.0] || sdtlseqdt0(skc3,xp)* -> .
% 6.14/6.34 23647[3:Res:64.2,23631.0] || aElementOf0(xp,xP) aElementOf0(skc3,xT)* -> .
% 6.14/6.34 23650[3:MRR:23647.0,23647.1,23131.0,23630.0] || -> .
% 6.14/6.34 % SZS output end Refutation
% 6.14/6.34 Formulae used in the proof : m__1123 m__1261 m__1144 m__1173 m__1244 m__ mARefl mDomSort m__1299 mEOfElem mDefEmpty mDefFix mDefSub mImgSort mDefLB mASymm mTrans
% 6.14/6.34
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