TSTP Solution File: SYN015-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 : Thu Jul 21 12:17:20 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 23:52:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 564 clauses, backtracked 230 clauses, performed 19 splits and kept 451 clauses.
% 0.20/0.47 SPASS allocated 63558 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.03 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.01 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.06 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 8, length 203 :
% 0.20/0.47 % SZS output start Refutation
% 0.20/0.47 1[0:Inp] || equal(n,m)** -> .
% 0.20/0.47 2[0:Inp] || equal(u,k) -> element(u,j)* equal(u,j).
% 0.20/0.47 3[0:Inp] || element(u,j)* -> equal(u,k) equal(u,j).
% 0.20/0.47 4[0:Inp] || element(u,m)* equal(f(u),m) -> equal(u,m).
% 0.20/0.47 5[0:Inp] || element(u,m)* equal(f(u),u) -> equal(u,m).
% 0.20/0.47 6[0:Inp] || element(u,m) -> equal(u,m) element(u,f(u))*.
% 0.20/0.47 7[0:Inp] || element(u,m) -> equal(u,m) element(f(u),u)*.
% 0.20/0.47 8[0:Inp] || element(u,v)*+ element(v,u)* -> equal(u,v) equal(u,m) element(v,m)* equal(v,m).
% 0.20/0.47 9[0:Inp] || equal(g(u),n) -> element(u,n)* equal(u,n).
% 0.20/0.47 10[0:Inp] || equal(g(u),u) -> element(u,n)* equal(u,n).
% 0.20/0.47 11[0:Inp] || -> element(u,n) equal(u,n) element(u,g(u))*.
% 0.20/0.47 12[0:Inp] || -> element(u,n) equal(u,n) element(g(u),u)*.
% 0.20/0.47 13[0:Inp] || element(u,v)*+ element(v,u)* element(v,n)* -> equal(u,v) equal(u,n) equal(v,n).
% 0.20/0.47 14[0:Inp] || equal(u,m) -> element(u,k)* equal(u,k).
% 0.20/0.47 15[0:Inp] || equal(u,n) -> element(u,k)* equal(u,k).
% 0.20/0.47 16[0:Inp] || element(u,k)* -> equal(u,n) equal(u,m) equal(u,k).
% 0.20/0.47 18[0:Res:12.2,3.0] || -> element(j,n)* equal(j,n) equal(g(j),k) equal(g(j),j).
% 0.20/0.47 19[0:MRR:18.3,10.0] || -> element(j,n)* equal(j,n) equal(g(j),k).
% 0.20/0.47 20[0:Res:7.2,3.0] || element(j,m)* -> equal(j,m) equal(f(j),k) equal(f(j),j).
% 0.20/0.47 21[0:MRR:20.3,5.1] || element(j,m)* -> equal(j,m) equal(f(j),k).
% 0.20/0.47 22[1:Spt:21.1] || -> equal(j,m)**.
% 0.20/0.47 23[1:Rew:22.0,2.1] || equal(u,k) -> element(u,m)* equal(u,j).
% 0.20/0.47 24[1:Rew:22.0,3.0] || element(u,m)* -> equal(u,k) equal(u,j).
% 0.20/0.47 25[1:Rew:22.0,19.0] || -> element(m,n)* equal(j,n) equal(g(j),k).
% 0.20/0.47 26[1:Rew:22.0,23.2] || equal(u,k) -> element(u,m)* equal(u,m).
% 0.20/0.47 27[1:Rew:22.0,24.2] || element(u,m)* -> equal(u,k) equal(u,m).
% 0.20/0.47 28[1:Rew:22.0,25.2,22.0,25.1] || -> element(m,n)* equal(n,m) equal(g(m),k).
% 0.20/0.47 29[1:MRR:28.1,1.0] || -> element(m,n)* equal(g(m),k).
% 0.20/0.47 35[0:Res:12.2,4.0] || equal(f(g(m)),m)** -> element(m,n) equal(n,m) equal(g(m),m).
% 0.20/0.47 38[1:Rew:29.1,35.3,29.1,35.0] || equal(f(k),m) -> element(m,n)* equal(n,m) equal(k,m).
% 0.20/0.47 39[1:MRR:38.2,1.0] || equal(f(k),m) -> element(m,n)* equal(k,m).
% 0.20/0.47 40[2:Spt:39.2] || -> equal(k,m)**.
% 0.20/0.47 42[2:Rew:40.0,15.1] || equal(u,n) -> element(u,m)* equal(u,k).
% 0.20/0.47 43[2:Rew:40.0,27.1] || element(u,m)* -> equal(u,m) equal(u,m).
% 0.20/0.47 49[2:Rew:40.0,42.2] || equal(u,n) -> element(u,m)* equal(u,m).
% 0.20/0.47 50[2:Obv:43.1] || element(u,m)* -> equal(u,m).
% 0.20/0.47 51[2:MRR:49.1,50.0] || equal(u,n)* -> equal(u,m).
% 0.20/0.47 57[2:EqR:51.0] || -> equal(n,m)**.
% 0.20/0.47 58[2:MRR:57.0,1.0] || -> .
% 0.20/0.47 59[2:Spt:58.0,39.2,40.0] || equal(k,m)** -> .
% 0.20/0.47 60[2:Spt:58.0,39.0,39.1] || equal(f(k),m) -> element(m,n)*.
% 0.20/0.47 77[0:Res:12.2,16.0] || -> element(k,n)* equal(k,n) equal(g(k),n) equal(g(k),m) equal(g(k),k).
% 0.20/0.47 78[0:Res:7.2,16.0] || element(k,m)* -> equal(k,m) equal(f(k),n) equal(f(k),m) equal(f(k),k).
% 0.20/0.47 79[0:MRR:77.2,77.4,9.0,10.0] || -> element(k,n)* equal(k,n) equal(g(k),m).
% 0.20/0.47 124[0:Res:6.2,8.0] || element(u,m) element(f(u),u)* -> equal(u,m) equal(f(u),u) equal(u,m) element(f(u),m)* equal(f(u),m).
% 0.20/0.47 125[0:Res:12.2,8.0] || element(u,g(u))* -> element(u,n) equal(u,n) equal(g(u),u) equal(g(u),m) element(u,m) equal(u,m).
% 0.20/0.47 132[0:Obv:124.2] || element(u,m) element(f(u),u)* -> equal(f(u),u) equal(u,m) element(f(u),m)* equal(f(u),m).
% 0.20/0.47 133[0:MRR:132.1,132.2,132.5,7.2,5.1,4.1] || element(u,m) -> equal(u,m) element(f(u),m)*.
% 0.20/0.47 165[0:MRR:125.0,125.3,11.2,10.0] || -> element(u,n)* equal(u,n) equal(g(u),m) element(u,m) equal(u,m).
% 0.20/0.47 213[1:Res:133.2,27.0] || element(u,m)* -> equal(u,m) equal(f(u),k) equal(f(u),m).
% 0.20/0.47 214[1:MRR:213.3,4.1] || element(u,m)* -> equal(u,m) equal(f(u),k).
% 0.20/0.47 219[1:Rew:214.2,5.1] || element(u,m)* equal(k,u) -> equal(u,m).
% 0.20/0.47 222[1:MRR:219.0,26.1] || equal(k,u)* -> equal(u,m).
% 0.20/0.47 223[1:EqR:222.0] || -> equal(k,m)**.
% 0.20/0.47 224[2:MRR:223.0,59.0] || -> .
% 0.20/0.47 225[1:Spt:224.0,21.1,22.0] || equal(j,m)** -> .
% 0.20/0.47 226[1:Spt:224.0,21.0,21.2] || element(j,m)* -> equal(f(j),k).
% 0.20/0.47 229[0:MRR:78.3,78.4,4.1,5.1] || element(k,m)* -> equal(k,m) equal(f(k),n).
% 0.20/0.47 231[2:Spt:79.1] || -> equal(k,n)**.
% 0.20/0.47 232[2:Rew:231.0,14.2] || equal(u,m) -> element(u,k)* equal(u,n).
% 0.20/0.47 237[2:Rew:231.0,3.1] || element(u,j)* -> equal(u,n) equal(u,j).
% 0.20/0.47 238[2:Rew:231.0,16.3] || element(u,k)* -> equal(u,n) equal(u,m) equal(u,n).
% 0.20/0.47 239[2:Rew:231.0,19.2] || -> element(j,n)* equal(j,n) equal(g(j),n).
% 0.20/0.47 241[2:Rew:231.0,232.1] || equal(u,m) -> element(u,n)* equal(u,n).
% 0.20/0.47 242[2:MRR:239.2,9.0] || -> element(j,n)* equal(j,n).
% 0.20/0.47 245[2:Obv:238.1] || element(u,k)* -> equal(u,m) equal(u,n).
% 0.20/0.47 246[2:Rew:231.0,245.0] || element(u,n)* -> equal(u,m) equal(u,n).
% 0.20/0.47 251[3:Spt:242.1] || -> equal(j,n)**.
% 0.20/0.47 254[3:Rew:251.0,237.0] || element(u,n)* -> equal(u,n) equal(u,j).
% 0.20/0.47 257[3:Rew:251.0,254.2] || element(u,n)* -> equal(u,n) equal(u,n).
% 0.20/0.47 258[3:Obv:257.1] || element(u,n)* -> equal(u,n).
% 0.20/0.47 263[3:MRR:241.1,258.0] || equal(u,m) -> equal(u,n)*.
% 0.20/0.47 272[3:SpL:263.1,1.0] || equal(u,m)* equal(u,m)* -> .
% 0.20/0.47 275[3:Obv:272.0] || equal(u,m)* -> .
% 0.20/0.47 276[3:AED:1.0,275.0] || -> .
% 0.20/0.47 277[3:Spt:276.0,242.1,251.0] || equal(j,n)** -> .
% 0.20/0.47 278[3:Spt:276.0,242.0] || -> element(j,n)*.
% 0.20/0.47 292[3:Res:278.0,246.0] || -> equal(j,m) equal(j,n)**.
% 0.20/0.47 293[3:MRR:292.0,292.1,225.0,277.0] || -> .
% 0.20/0.47 294[2:Spt:293.0,79.1,231.0] || equal(k,n)** -> .
% 0.20/0.47 295[2:Spt:293.0,79.0,79.2] || -> element(k,n)* equal(g(k),m).
% 0.20/0.47 296[2:Res:295.0,8.0] || element(n,k)* -> equal(g(k),m) equal(k,n) equal(k,m) element(n,m) equal(n,m).
% 0.20/0.47 297[2:MRR:296.5,1.0] || element(n,k)* -> equal(g(k),m) equal(k,n) equal(k,m) element(n,m).
% 0.20/0.47 298[2:MRR:297.2,294.0] || element(n,k)* -> equal(g(k),m) equal(k,m) element(n,m).
% 0.20/0.47 301[3:Spt:19.1] || -> equal(j,n)**.
% 0.20/0.47 303[3:Rew:301.0,226.0] || element(n,m)* -> equal(f(j),k).
% 0.20/0.47 304[3:Rew:301.0,2.1] || equal(u,k) -> element(u,n)* equal(u,j).
% 0.20/0.47 305[3:Rew:301.0,3.0] || element(u,n)* -> equal(u,k) equal(u,j).
% 0.20/0.47 306[3:Rew:301.0,303.1] || element(n,m)* -> equal(f(n),k).
% 0.20/0.47 307[3:Rew:301.0,304.2] || equal(u,k) -> element(u,n)* equal(u,n).
% 0.20/0.47 308[3:Rew:301.0,305.2] || element(u,n)* -> equal(u,k) equal(u,n).
% 0.20/0.47 319[4:Spt:229.1] || -> equal(k,m)**.
% 0.20/0.47 323[4:Rew:319.0,15.1] || equal(u,n) -> element(u,m)* equal(u,k).
% 0.20/0.47 324[4:Rew:319.0,308.1] || element(u,n)* -> equal(u,m) equal(u,n).
% 0.20/0.47 325[4:Rew:319.0,307.0] || equal(u,m) -> element(u,n)* equal(u,n).
% 0.20/0.47 326[4:Rew:319.0,306.1] || element(n,m)* -> equal(f(n),m).
% 0.20/0.47 327[4:Rew:319.0,16.0] || element(u,m)* -> equal(u,n) equal(u,m) equal(u,k).
% 0.20/0.47 331[4:Rew:319.0,323.2] || equal(u,n) -> element(u,m)* equal(u,m).
% 0.20/0.47 332[4:MRR:165.0,324.0] || -> equal(u,n) equal(g(u),m) element(u,m)* equal(u,m).
% 0.20/0.47 334[4:Rew:319.0,327.3] || element(u,m)* -> equal(u,n) equal(u,m) equal(u,m).
% 0.20/0.47 335[4:Obv:334.2] || element(u,m)* -> equal(u,n) equal(u,m).
% 0.20/0.47 336[4:MRR:332.0,331.0] || -> equal(g(u),m) element(u,m)* equal(u,m).
% 0.20/0.47 340[4:Res:331.1,326.0] || equal(n,n) -> equal(n,m) equal(f(n),m)**.
% 0.20/0.47 341[4:Obv:340.0] || -> equal(n,m) equal(f(n),m)**.
% 0.20/0.47 342[4:MRR:341.0,1.0] || -> equal(f(n),m)**.
% 0.20/0.47 351[4:Res:336.1,335.0] || -> equal(g(u),m)** equal(u,m) equal(u,n) equal(u,m).
% 0.20/0.47 352[4:Obv:351.1] || -> equal(g(u),m)** equal(u,n) equal(u,m).
% 0.20/0.47 355[4:SpR:352.0,11.2] || -> equal(u,n) equal(u,m) element(u,n)* equal(u,n) element(u,m).
% 0.20/0.47 358[4:Obv:355.0] || -> equal(u,m) element(u,n)* equal(u,n) element(u,m).
% 0.20/0.47 359[4:MRR:358.0,325.0] || -> element(u,n)* equal(u,n) element(u,m).
% 0.20/0.47 363[4:Res:359.0,324.0] || -> equal(u,n) element(u,m)* equal(u,m) equal(u,n).
% 0.20/0.47 364[4:Obv:363.0] || -> element(u,m)* equal(u,m) equal(u,n).
% 0.20/0.47 365[4:MRR:364.0,335.0] || -> equal(u,m) equal(u,n)*.
% 0.20/0.47 386[4:SpR:365.1,342.0] || -> equal(u,m) equal(f(u),m)**.
% 0.20/0.47 394[4:Rew:386.1,4.1] || element(u,m)* equal(m,m) -> equal(u,m).
% 0.20/0.47 397[4:Obv:394.1] || element(u,m)* -> equal(u,m).
% 0.20/0.47 398[4:MRR:331.1,397.0] || equal(u,n)* -> equal(u,m).
% 0.20/0.47 408[4:EqR:398.0] || -> equal(n,m)**.
% 0.20/0.47 411[4:MRR:408.0,1.0] || -> .
% 0.20/0.47 412[4:Spt:411.0,229.1,319.0] || equal(k,m)** -> .
% 0.20/0.47 413[4:Spt:411.0,229.0,229.2] || element(k,m)* -> equal(f(k),n).
% 0.20/0.47 414[4:MRR:298.2,412.0] || element(n,k)* -> equal(g(k),m) element(n,m).
% 0.20/0.47 421[5:Spt:414.1] || -> equal(g(k),m)**.
% 0.20/0.48 423[5:SpR:421.0,11.2] || -> element(k,n)* equal(k,n) element(k,m).
% 0.20/0.48 426[5:MRR:423.1,294.0] || -> element(k,n)* element(k,m).
% 0.20/0.48 428[6:Spt:426.0] || -> element(k,n)*.
% 0.20/0.48 458[6:Res:428.0,8.0] || element(n,k)* -> equal(k,n) equal(k,m) element(n,m) equal(n,m).
% 0.20/0.48 464[0:Res:15.1,8.0] || equal(u,n) element(k,u)* -> equal(u,k) equal(u,k) equal(u,m) element(k,m)* equal(k,m).
% 0.20/0.48 469[6:MRR:458.1,458.2,458.4,294.0,412.0,1.0] || element(n,k)* -> element(n,m).
% 0.20/0.48 470[0:Obv:464.2] || equal(u,n) element(k,u)* -> equal(u,k) equal(u,m) element(k,m)* equal(k,m).
% 0.20/0.48 476[6:Res:15.1,469.0] || equal(n,n) -> equal(k,n) element(n,m)*.
% 0.20/0.48 477[6:Obv:476.0] || -> equal(k,n) element(n,m)*.
% 0.20/0.48 478[6:MRR:477.0,294.0] || -> element(n,m)*.
% 0.20/0.48 479[6:MRR:306.0,478.0] || -> equal(f(n),k)**.
% 0.20/0.48 485[6:SpR:479.0,133.2] || element(n,m) -> equal(n,m) element(k,m)*.
% 0.20/0.48 490[6:MRR:485.0,485.1,478.0,1.0] || -> element(k,m)*.
% 0.20/0.48 506[0:Res:14.1,13.0] || equal(u,m) element(k,u)* element(k,n)* -> equal(u,k) equal(u,k) equal(u,n) equal(k,n).
% 0.20/0.48 512[0:Obv:506.3] || equal(u,m) element(k,u)* element(k,n)* -> equal(u,k) equal(u,n) equal(k,n).
% 0.20/0.48 513[6:MRR:512.2,512.5,428.0,294.0] || equal(u,m) element(k,u)* -> equal(u,k) equal(u,n).
% 0.20/0.48 545[6:Res:490.0,513.1] || equal(m,m) -> equal(k,m)** equal(n,m).
% 0.20/0.48 554[6:Obv:545.0] || -> equal(k,m)** equal(n,m).
% 0.20/0.48 555[6:MRR:554.0,554.1,412.0,1.0] || -> .
% 0.20/0.48 556[6:Spt:555.0,426.0,428.0] || element(k,n)* -> .
% 0.20/0.48 557[6:Spt:555.0,426.1] || -> element(k,m)*.
% 0.20/0.48 565[0:Obv:506.3] || equal(u,m) element(k,u)* element(k,n)* -> equal(u,k) equal(u,n) equal(k,n).
% 0.20/0.48 578[6:Res:307.1,556.0] || equal(k,k)* -> equal(k,n).
% 0.20/0.48 579[6:Obv:578.0] || -> equal(k,n)**.
% 0.20/0.48 580[6:MRR:579.0,294.0] || -> .
% 0.20/0.48 584[5:Spt:580.0,414.1,421.0] || equal(g(k),m)** -> .
% 0.20/0.48 585[5:Spt:580.0,414.0,414.2] || element(n,k)* -> element(n,m).
% 0.20/0.48 586[5:MRR:295.1,584.0] || -> element(k,n)*.
% 0.20/0.48 587[2:MRR:565.5,294.0] || equal(u,m) element(k,u)* element(k,n)* -> equal(u,k) equal(u,n).
% 0.20/0.48 588[5:MRR:587.2,586.0] || equal(u,m) element(k,u)* -> equal(u,k) equal(u,n).
% 0.20/0.48 591[5:Res:15.1,585.0] || equal(n,n) -> equal(k,n) element(n,m)*.
% 0.20/0.48 592[5:Obv:591.0] || -> equal(k,n) element(n,m)*.
% 0.20/0.48 593[5:MRR:592.0,294.0] || -> element(n,m)*.
% 0.20/0.48 594[5:MRR:306.0,593.0] || -> equal(f(n),k)**.
% 0.20/0.48 604[5:SpR:594.0,133.2] || element(n,m) -> equal(n,m) element(k,m)*.
% 0.20/0.48 609[5:MRR:604.0,604.1,593.0,1.0] || -> element(k,m)*.
% 0.20/0.48 646[5:Res:609.0,588.1] || equal(m,m) -> equal(k,m)** equal(n,m).
% 0.20/0.48 656[5:Obv:646.0] || -> equal(k,m)** equal(n,m).
% 0.20/0.48 657[5:MRR:656.0,656.1,412.0,1.0] || -> .
% 0.20/0.48 658[3:Spt:657.0,19.1,301.0] || equal(j,n)** -> .
% 0.20/0.48 659[3:Spt:657.0,19.0,19.2] || -> element(j,n)* equal(g(j),k).
% 0.20/0.48 664[4:Spt:295.0] || -> element(k,n)*.
% 0.20/0.48 665[4:MRR:587.2,664.0] || equal(u,m) element(k,u)* -> equal(u,k) equal(u,n).
% 0.20/0.48 667[4:Res:664.0,8.0] || element(n,k)* -> equal(k,n) equal(k,m) element(n,m) equal(n,m).
% 0.20/0.48 668[4:MRR:667.1,667.4,294.0,1.0] || element(n,k)* -> equal(k,m) element(n,m).
% 0.20/0.48 671[5:Spt:668.1] || -> equal(k,m)**.
% 0.20/0.48 674[5:Rew:671.0,16.3] || element(u,k)* -> equal(u,n) equal(u,m) equal(u,m).
% 0.20/0.48 676[5:Rew:671.0,15.2] || equal(u,n) -> element(u,k)* equal(u,m).
% 0.20/0.48 684[5:Rew:671.0,676.1] || equal(u,n) -> element(u,m)* equal(u,m).
% 0.20/0.48 685[5:Obv:674.2] || element(u,k)* -> equal(u,n) equal(u,m).
% 0.20/0.48 686[5:Rew:671.0,685.0] || element(u,m)* -> equal(u,n) equal(u,m).
% 0.20/0.48 707[5:Res:133.2,686.0] || element(u,m)* -> equal(u,m) equal(f(u),n) equal(f(u),m).
% 0.20/0.48 711[5:MRR:707.3,4.1] || element(u,m)* -> equal(u,m) equal(f(u),n).
% 0.20/0.48 716[5:Rew:711.2,5.1] || element(u,m)* equal(n,u) -> equal(u,m).
% 0.20/0.48 719[5:MRR:716.0,684.1] || equal(n,u)* -> equal(u,m).
% 0.20/0.48 720[5:EqR:719.0] || -> equal(n,m)**.
% 0.20/0.48 721[5:MRR:720.0,1.0] || -> .
% 0.20/0.48 722[5:Spt:721.0,668.1,671.0] || equal(k,m)** -> .
% 0.20/0.48 723[5:Spt:721.0,668.0,668.2] || element(n,k)* -> element(n,m).
% 0.20/0.48 725[5:MRR:470.5,722.0] || equal(u,n)+ element(k,u)* -> equal(u,k) equal(u,m) element(k,m)*.
% 0.20/0.48 791[6:Spt:725.0,725.1,725.2,725.3] || equal(u,n) element(k,u)* -> equal(u,k) equal(u,m).
% 0.20/0.48 800[6:Res:664.0,791.1] || equal(n,n) -> equal(k,n)** equal(n,m).
% 0.20/0.48 801[6:Obv:800.0] || -> equal(k,n)** equal(n,m).
% 0.20/0.48 802[6:MRR:801.0,801.1,294.0,1.0] || -> .
% 0.20/0.48 816[6:Spt:802.0,725.4] || -> element(k,m)*.
% 0.20/0.48 822[6:Res:816.0,665.1] || equal(m,m) -> equal(k,m)** equal(n,m).
% 0.20/0.48 825[6:Obv:822.0] || -> equal(k,m)** equal(n,m).
% 0.20/0.48 826[6:MRR:825.0,825.1,722.0,1.0] || -> .
% 0.20/0.48 828[4:Spt:826.0,295.0,664.0] || element(k,n)* -> .
% 0.20/0.48 829[4:Spt:826.0,295.1] || -> equal(g(k),m)**.
% 0.20/0.48 832[4:SpR:829.0,11.2] || -> element(k,n)* equal(k,n) element(k,m).
% 0.20/0.48 839[4:MRR:832.1,294.0] || -> element(k,n)* element(k,m).
% 0.20/0.48 840[4:MRR:839.0,828.0] || -> element(k,m)*.
% 0.20/0.48 841[4:MRR:229.0,840.0] || -> equal(k,m) equal(f(k),n)**.
% 0.20/0.48 862[4:Res:10.1,828.0] || equal(g(k),k)** -> equal(k,n).
% 0.20/0.48 864[4:Rew:829.0,862.0] || equal(k,m)** -> equal(k,n).
% 0.20/0.48 865[4:MRR:864.1,294.0] || equal(k,m)** -> .
% 0.20/0.48 866[4:MRR:841.0,865.0] || -> equal(f(k),n)**.
% 0.20/0.48 873[4:SpR:866.0,6.2] || element(k,m) -> equal(k,m) element(k,n)*.
% 0.20/0.48 879[4:MRR:873.0,873.1,873.2,840.0,865.0,828.0] || -> .
% 0.20/0.48 % SZS output end Refutation
% 0.20/0.48 Formulae used in the proof : c_1 c_2 c_3 c_4 c_5 c_6 c_7 c_8 c_9 c_10 c_11 c_12 c_13 c_14 c_15 c_16
% 0.20/0.48
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