TSTP Solution File: GEO546+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO546+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 : Sat Jul 16 06:25:10 EDT 2022
% Result : Theorem 20.23s 20.42s
% Output : Refutation 20.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO546+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n016.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 : Sat Jun 18 15:21:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 20.23/20.42
% 20.23/20.42 SPASS V 3.9
% 20.23/20.42 SPASS beiseite: Proof found.
% 20.23/20.42 % SZS status Theorem
% 20.23/20.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.23/20.42 SPASS derived 22080 clauses, backtracked 6129 clauses, performed 2 splits and kept 18210 clauses.
% 20.23/20.42 SPASS allocated 103866 KBytes.
% 20.23/20.42 SPASS spent 0:0:20.05 on the problem.
% 20.23/20.42 0:00:00.04 for the input.
% 20.23/20.42 0:00:00.22 for the FLOTTER CNF translation.
% 20.23/20.42 0:00:00.41 for inferences.
% 20.23/20.42 0:00:00.23 for the backtracking.
% 20.23/20.42 0:0:18.80 for the reduction.
% 20.23/20.42
% 20.23/20.42
% 20.23/20.42 Here is a proof with depth 17, length 235 :
% 20.23/20.42 % SZS output start Refutation
% 20.23/20.42 1[0:Inp] || -> coll(skc7,skc11,skc10)*.
% 20.23/20.42 2[0:Inp] || -> coll(skc8,skc11,skc9)*.
% 20.23/20.42 3[0:Inp] || -> coll(skc9,skc10,skc6)*.
% 20.23/20.42 4[0:Inp] || -> coll(skc8,skc6,skc7)*.
% 20.23/20.42 5[0:Inp] || -> perp(skc7,skc6,skc11,skc10)*.
% 20.23/20.42 6[0:Inp] || -> perp(skc9,skc11,skc10,skc6)*.
% 20.23/20.42 7[0:Inp] || perp(skc10,skc8,skc11,skc6)* -> .
% 20.23/20.42 8[0:Inp] || coll(u,v,w)*+ -> coll(u,w,v)*.
% 20.23/20.42 9[0:Inp] || coll(u,v,w)*+ -> coll(v,u,w)*.
% 20.23/20.42 12[0:Inp] || para(u,v,u,w)* -> coll(u,v,w).
% 20.23/20.42 13[0:Inp] || midp(u,v,w) -> cong(u,v,u,w)*.
% 20.23/20.42 14[0:Inp] || para(u,v,w,x)*+ -> para(u,v,x,w)*.
% 20.23/20.42 15[0:Inp] || para(u,v,w,x)*+ -> para(w,x,u,v)*.
% 20.23/20.42 16[0:Inp] || perp(u,v,w,x)*+ -> perp(u,v,x,w)*.
% 20.23/20.42 17[0:Inp] || perp(u,v,w,x)*+ -> perp(w,x,u,v)*.
% 20.23/20.42 19[0:Inp] || cyclic(u,v,w,x)*+ -> cyclic(u,w,v,x)*.
% 20.23/20.42 20[0:Inp] || cyclic(u,v,w,x)*+ -> cyclic(v,u,w,x)*.
% 20.23/20.42 21[0:Inp] || cong(u,v,w,x)*+ -> cong(u,v,x,w)*.
% 20.23/20.42 22[0:Inp] || cong(u,v,w,x)*+ -> cong(w,x,u,v)*.
% 20.23/20.42 25[0:Inp] || coll(u,v,w)*+ coll(u,v,x)* -> coll(x,w,u)*.
% 20.23/20.42 32[0:Inp] || eqangle(u,v,w,x,y,z,w,x)* -> para(u,v,y,z).
% 20.23/20.42 33[0:Inp] || para(u,v,w,x) -> eqangle(u,v,y,z,w,x,y,z)*.
% 20.23/20.42 34[0:Inp] || cyclic(u,v,w,x) -> eqangle(w,u,w,v,x,u,x,v)*.
% 20.23/20.42 36[0:Inp] || cong(u,v,u,w) -> eqangle(u,v,v,w,v,w,u,w)*.
% 20.23/20.42 38[0:Inp] || coll(u,v,w) cong(u,v,u,w)* -> midp(u,v,w).
% 20.23/20.42 39[0:Inp] || midp(u,v,w)* perp(v,x,x,w)*+ -> cong(v,u,x,u)*.
% 20.23/20.42 41[0:Inp] || midp(u,v,w) perp(x,u,v,w)*+ -> cong(x,v,x,w)*.
% 20.23/20.42 43[0:Inp] || perp(u,v,w,x)*+ perp(y,z,u,v)* -> para(y,z,w,x)*.
% 20.23/20.42 46[0:Inp] || cyclic(u,v,w,x)*+ cyclic(u,v,w,y)* -> cyclic(v,w,y,x)*.
% 20.23/20.42 48[0:Inp] || cong(u,v,w,v)*+ cong(u,x,w,x)* -> perp(u,w,x,v)*.
% 20.23/20.42 54[0:Inp] || eqangle(u,v,w,x,y,z,x1,x2)*+ -> eqangle(w,x,u,v,x1,x2,y,z)*.
% 20.23/20.42 56[0:Inp] || eqangle(u,v,w,x,y,z,x1,x2)*+ -> eqangle(u,v,y,z,w,x,x1,x2)*.
% 20.23/20.42 61[0:Inp] || eqangle(u,v,u,w,x,v,x,w)* -> coll(u,x,v) cyclic(v,w,u,x).
% 20.23/20.42 74[0:Inp] || eqangle(u,v,w,x,w,x,u,v)* -> para(u,v,w,x) perp(u,v,w,x).
% 20.23/20.42 78[0:Inp] || coll(u,v,w) eqangle(u,x,u,w,v,x,v,w)* -> cyclic(x,w,u,v).
% 20.23/20.42 87[0:Inp] || midp(u,v,w)* para(v,x,w,y)*+ para(v,y,w,x)* -> midp(u,y,x)*.
% 20.23/20.42 89[0:Inp] || para(u,v,w,x) cyclic(u,v,w,x) -> eqangle(u,x,w,x,w,x,w,v)*.
% 20.23/20.42 94[0:Inp] || cyclic(u,v,w,x)*+ cong(u,x,v,x)* cong(u,w,v,w)* -> perp(w,u,u,x)*.
% 20.23/20.42 120[0:Inp] || cyclic(u,v,w,x) cyclic(u,v,w,y) cyclic(u,v,w,z) eqangle(w,u,w,v,z,x,z,y)* -> cong(u,v,x,y).
% 20.23/20.42 122[0:Res:4.0,25.0] || coll(skc8,skc6,u)* -> coll(skc7,u,skc8).
% 20.23/20.42 146[0:Res:3.0,8.0] || -> coll(skc9,skc6,skc10)*.
% 20.23/20.42 169[0:Res:2.0,8.0] || -> coll(skc8,skc9,skc11)*.
% 20.23/20.42 192[0:Res:1.0,8.0] || -> coll(skc7,skc10,skc11)*.
% 20.23/20.42 193[0:Res:1.0,9.0] || -> coll(skc11,skc7,skc10)*.
% 20.23/20.42 195[0:Res:1.0,25.1] || coll(skc7,skc11,u)*+ -> coll(u,skc10,skc7)*.
% 20.23/20.42 223[0:Res:6.0,17.0] || -> perp(skc10,skc6,skc9,skc11)*.
% 20.23/20.42 240[0:Res:5.0,43.0] || perp(skc11,skc10,u,v) -> para(skc7,skc6,u,v)*.
% 20.23/20.42 241[0:Res:5.0,16.0] || -> perp(skc7,skc6,skc10,skc11)*.
% 20.23/20.42 242[0:Res:5.0,17.0] || -> perp(skc11,skc10,skc7,skc6)*.
% 20.23/20.42 247[0:Res:5.0,43.1] || perp(u,v,skc7,skc6) -> para(u,v,skc11,skc10)*.
% 20.23/20.42 253[0:Res:4.0,122.0] || -> coll(skc7,skc7,skc8)*.
% 20.23/20.42 254[0:Res:1.0,195.0] || -> coll(skc10,skc10,skc7)*.
% 20.23/20.42 263[0:Res:146.0,9.0] || -> coll(skc6,skc9,skc10)*.
% 20.23/20.42 289[0:Res:254.0,8.0] || -> coll(skc10,skc7,skc10)*.
% 20.23/20.42 291[0:Res:253.0,8.0] || -> coll(skc7,skc8,skc7)*.
% 20.23/20.42 370[0:Res:241.0,17.0] || -> perp(skc10,skc11,skc7,skc6)*.
% 20.23/20.42 380[0:Res:242.0,16.0] || -> perp(skc11,skc10,skc6,skc7)*.
% 20.23/20.42 381[0:Res:370.0,16.0] || -> perp(skc10,skc11,skc6,skc7)*.
% 20.23/20.42 384[0:Res:223.0,16.0] || -> perp(skc10,skc6,skc11,skc9)*.
% 20.23/20.42 388[0:Res:380.0,17.0] || -> perp(skc6,skc7,skc11,skc10)*.
% 20.23/20.42 390[0:Res:381.0,17.0] || -> perp(skc6,skc7,skc10,skc11)*.
% 20.23/20.42 392[0:Res:384.0,17.0] || -> perp(skc11,skc9,skc10,skc6)*.
% 20.23/20.42 413[0:Res:169.0,25.0] || coll(skc8,skc9,u)*+ -> coll(u,skc11,skc8)*.
% 20.23/20.42 418[0:Res:192.0,25.0] || coll(skc7,skc10,u)*+ -> coll(u,skc11,skc7)*.
% 20.23/20.42 421[0:Res:193.0,25.0] || coll(skc11,skc7,u)*+ -> coll(u,skc10,skc11)*.
% 20.23/20.42 423[0:Res:263.0,25.0] || coll(skc6,skc9,u)*+ -> coll(u,skc10,skc6)*.
% 20.23/20.42 431[0:Res:254.0,25.0] || coll(skc10,skc10,u)*+ -> coll(u,skc7,skc10)*.
% 20.23/20.42 434[0:Res:289.0,25.0] || coll(skc10,skc7,u)*+ -> coll(u,skc10,skc10)*.
% 20.23/20.42 439[0:Res:291.0,25.0] || coll(skc7,skc8,u)*+ -> coll(u,skc7,skc7)*.
% 20.23/20.42 451[0:Res:169.0,413.0] || -> coll(skc11,skc11,skc8)*.
% 20.23/20.42 454[0:Res:451.0,8.0] || -> coll(skc11,skc8,skc11)*.
% 20.23/20.42 456[0:Res:454.0,25.0] || coll(skc11,skc8,u)*+ -> coll(u,skc11,skc11)*.
% 20.23/20.42 489[0:Res:192.0,418.0] || -> coll(skc11,skc11,skc7)*.
% 20.23/20.42 494[0:Res:489.0,8.0] || -> coll(skc11,skc7,skc11)*.
% 20.23/20.42 526[0:Res:193.0,421.0] || -> coll(skc10,skc10,skc11)*.
% 20.23/20.42 527[0:Res:494.0,421.0] || -> coll(skc11,skc10,skc11)*.
% 20.23/20.42 533[0:Res:527.0,8.0] || -> coll(skc11,skc11,skc10)*.
% 20.23/20.42 563[0:Res:263.0,423.0] || -> coll(skc10,skc10,skc6)*.
% 20.23/20.42 614[0:Res:36.1,32.0] || cong(u,u,u,v)* -> para(u,u,u,v).
% 20.23/20.42 616[0:Res:34.1,32.0] || cyclic(u,v,w,w)*+ -> para(w,u,w,u)*.
% 20.23/20.42 637[0:Res:388.0,41.1] || midp(skc7,skc11,skc10) -> cong(skc6,skc11,skc6,skc10)*.
% 20.23/20.42 638[0:Res:241.0,41.1] || midp(skc6,skc10,skc11) -> cong(skc7,skc10,skc7,skc11)*.
% 20.23/20.42 660[0:Res:563.0,431.0] || -> coll(skc6,skc7,skc10)*.
% 20.23/20.42 666[0:Res:660.0,9.0] || -> coll(skc7,skc6,skc10)*.
% 20.23/20.42 679[0:Res:666.0,8.0] || -> coll(skc7,skc10,skc6)*.
% 20.23/20.42 705[0:Res:679.0,418.0] || -> coll(skc6,skc11,skc7)*.
% 20.23/20.42 727[0:Res:705.0,9.0] || -> coll(skc11,skc6,skc7)*.
% 20.23/20.42 759[0:Res:727.0,8.0] || -> coll(skc11,skc7,skc6)*.
% 20.23/20.42 772[0:Res:392.0,43.0] || perp(u,v,skc11,skc9) -> para(u,v,skc10,skc6)*.
% 20.23/20.42 774[0:Res:370.0,43.0] || perp(u,v,skc10,skc11) -> para(u,v,skc7,skc6)*.
% 20.23/20.42 778[0:Res:388.0,43.0] || perp(u,v,skc6,skc7) -> para(u,v,skc11,skc10)*.
% 20.23/20.42 782[0:Res:390.0,43.0] || perp(u,v,skc6,skc7) -> para(u,v,skc10,skc11)*.
% 20.23/20.42 790[0:Res:759.0,421.0] || -> coll(skc6,skc10,skc11)*.
% 20.23/20.42 894[0:Res:289.0,434.0] || -> coll(skc10,skc10,skc10)*.
% 20.23/20.42 1036[0:Res:33.1,61.0] || para(u,v,u,v)*+ -> coll(u,u,v) cyclic(v,w,u,u)*.
% 20.23/20.42 1125[0:Res:33.1,56.0] || para(u,v,w,x) -> eqangle(u,v,w,x,y,z,y,z)*.
% 20.23/20.42 1164[0:Res:33.1,54.0] || para(u,v,w,x) -> eqangle(y,z,u,v,y,z,w,x)*.
% 20.23/20.42 1261[0:Res:291.0,439.0] || -> coll(skc7,skc7,skc7)*.
% 20.23/20.42 1368[0:Res:33.1,78.1] || para(u,v,u,v)*+ coll(u,u,w) -> cyclic(v,w,u,u)*.
% 20.23/20.42 1425[0:Res:36.1,74.0] || cong(u,v,u,v)*+ -> para(u,v,v,v)* perp(u,v,v,v).
% 20.23/20.42 1431[0:Res:454.0,456.0] || -> coll(skc11,skc11,skc11)*.
% 20.23/20.42 2631[0:Res:33.1,120.3] || para(u,v,u,w)*+ cyclic(v,x,u,w)* cyclic(v,x,u,x)* cyclic(v,x,u,u)* -> cong(v,x,w,x)*.
% 20.23/20.42 2633[0:Res:89.2,120.3] || para(u,v,u,w)+ cyclic(u,v,u,w)* cyclic(w,w,u,w)* cyclic(w,w,u,v)* cyclic(w,w,u,u)* -> cong(w,w,w,v)*.
% 20.23/20.42 2634[0:Res:34.1,120.3] || cyclic(u,v,w,x)* cyclic(u,v,w,u)* cyclic(u,v,w,v)* cyclic(u,v,w,x)* -> cong(u,v,u,v)*.
% 20.23/20.42 2636[0:Obv:2634.0] || cyclic(u,v,w,u)* cyclic(u,v,w,v)* cyclic(u,v,w,x)* -> cong(u,v,u,v)*.
% 20.23/20.42 2637[0:Con:2636.2] || cyclic(u,v,w,u)*+ cyclic(u,v,w,v)* -> cong(u,v,u,v)*.
% 20.23/20.42 2844[0:Res:240.1,14.0] || perp(skc11,skc10,u,v) -> para(skc7,skc6,v,u)*.
% 20.23/20.42 2919[0:Res:247.1,15.0] || perp(u,v,skc7,skc6) -> para(skc11,skc10,u,v)*.
% 20.23/20.42 3041[0:Res:637.1,22.0] || midp(skc7,skc11,skc10) -> cong(skc6,skc10,skc6,skc11)*.
% 20.23/20.42 3057[0:Res:638.1,21.0] || midp(skc6,skc10,skc11) -> cong(skc7,skc10,skc11,skc7)*.
% 20.23/20.42 3075[0:Res:13.1,614.0] || midp(u,u,v) -> para(u,u,u,v)*.
% 20.23/20.42 3337[0:Res:3041.1,38.1] || midp(skc7,skc11,skc10)* coll(skc6,skc10,skc11) -> midp(skc6,skc10,skc11).
% 20.23/20.42 3341[0:MRR:3337.1,790.0] || midp(skc7,skc11,skc10)* -> midp(skc6,skc10,skc11).
% 20.23/20.42 3349[0:Res:3057.1,22.0] || midp(skc6,skc10,skc11) -> cong(skc11,skc7,skc7,skc10)*.
% 20.23/20.42 3532[0:Res:3349.1,21.0] || midp(skc6,skc10,skc11) -> cong(skc11,skc7,skc10,skc7)*.
% 20.23/20.42 3687[0:Res:3532.1,48.0] || midp(skc6,skc10,skc11) cong(skc11,u,skc10,u)* -> perp(skc11,skc10,u,skc7).
% 20.23/20.42 4089[0:Res:3075.1,14.0] || midp(u,u,v) -> para(u,u,v,u)*.
% 20.23/20.42 4311[0:Res:4089.1,15.0] || midp(u,u,v) -> para(v,u,u,u)*.
% 20.23/20.42 4666[0:Res:1125.1,61.0] || para(u,v,u,v)* -> coll(u,w,v) cyclic(v,v,u,w)*.
% 20.23/20.42 4677[0:Res:1125.1,78.1] || para(u,v,u,v)* coll(u,w,v) -> cyclic(v,v,u,w)*.
% 20.23/20.42 4693[0:MRR:4677.1,4666.1] || para(u,v,u,v)*+ -> cyclic(v,v,u,w)*.
% 20.23/20.42 5006[0:Res:1164.1,32.0] || para(u,v,u,v)*+ -> para(w,x,w,x)*.
% 20.23/20.42 5593[0:Res:778.1,1368.0] || perp(skc11,skc10,skc6,skc7) coll(skc11,skc11,u) -> cyclic(skc10,u,skc11,skc11)*.
% 20.23/20.42 5597[0:Res:772.1,1368.0] || perp(skc10,skc6,skc11,skc9) coll(skc10,skc10,u) -> cyclic(skc6,u,skc10,skc10)*.
% 20.23/20.42 5599[0:Res:774.1,1368.0] || perp(skc7,skc6,skc10,skc11) coll(skc7,skc7,u) -> cyclic(skc6,u,skc7,skc7)*.
% 20.23/20.42 5603[0:Res:782.1,1368.0] || perp(skc10,skc11,skc6,skc7) coll(skc10,skc10,u) -> cyclic(skc11,u,skc10,skc10)*.
% 20.23/20.42 5619[0:MRR:5593.0,380.0] || coll(skc11,skc11,u) -> cyclic(skc10,u,skc11,skc11)*.
% 20.23/20.42 5621[0:MRR:5597.0,384.0] || coll(skc10,skc10,u) -> cyclic(skc6,u,skc10,skc10)*.
% 20.23/20.42 5622[0:MRR:5599.0,241.0] || coll(skc7,skc7,u) -> cyclic(skc6,u,skc7,skc7)*.
% 20.23/20.42 5624[0:MRR:5603.0,381.0] || coll(skc10,skc10,u) -> cyclic(skc11,u,skc10,skc10)*.
% 20.23/20.42 5667[0:Res:5619.1,20.0] || coll(skc11,skc11,u) -> cyclic(u,skc10,skc11,skc11)*.
% 20.23/20.42 5668[0:Res:5619.1,616.0] || coll(skc11,skc11,u)*+ -> para(skc11,skc10,skc11,skc10)*.
% 20.23/20.42 5671[0:Res:451.0,5668.0] || -> para(skc11,skc10,skc11,skc10)*.
% 20.23/20.42 5679[0:Res:5671.0,14.0] || -> para(skc11,skc10,skc10,skc11)*.
% 20.23/20.42 5694[0:Res:5679.0,15.0] || -> para(skc10,skc11,skc11,skc10)*.
% 20.23/20.42 5715[0:Res:5694.0,14.0] || -> para(skc10,skc11,skc10,skc11)*.
% 20.23/20.42 5911[0:Res:5621.1,20.0] || coll(skc10,skc10,u) -> cyclic(u,skc6,skc10,skc10)*.
% 20.23/20.42 5912[0:Res:5621.1,616.0] || coll(skc10,skc10,u)*+ -> para(skc10,skc6,skc10,skc6)*.
% 20.23/20.42 5915[0:Res:254.0,5912.0] || -> para(skc10,skc6,skc10,skc6)*.
% 20.23/20.42 5924[0:Res:5915.0,14.0] || -> para(skc10,skc6,skc6,skc10)*.
% 20.23/20.42 5979[0:Res:5924.0,15.0] || -> para(skc6,skc10,skc10,skc6)*.
% 20.23/20.42 5991[0:Res:5979.0,14.0] || -> para(skc6,skc10,skc6,skc10)*.
% 20.23/20.42 6015[0:Res:5991.0,87.1] || midp(u,skc6,skc6) para(skc6,skc10,skc6,skc10)* -> midp(u,skc10,skc10)*.
% 20.23/20.42 6017[0:MRR:6015.1,5991.0] || midp(u,skc6,skc6) -> midp(u,skc10,skc10)*.
% 20.23/20.42 6056[0:Res:5622.1,20.0] || coll(skc7,skc7,u) -> cyclic(u,skc6,skc7,skc7)*.
% 20.23/20.42 6057[0:Res:5622.1,616.0] || coll(skc7,skc7,u)*+ -> para(skc7,skc6,skc7,skc6)*.
% 20.23/20.42 6059[0:Res:253.0,6057.0] || -> para(skc7,skc6,skc7,skc6)*.
% 20.23/20.42 6068[0:Res:6059.0,14.0] || -> para(skc7,skc6,skc6,skc7)*.
% 20.23/20.42 6078[0:Res:6059.0,87.1] || midp(u,skc7,skc7)* para(skc7,skc6,skc7,skc6)* -> midp(u,skc6,skc6).
% 20.23/20.42 6080[0:MRR:6078.1,6059.0] || midp(u,skc7,skc7)* -> midp(u,skc6,skc6).
% 20.23/20.42 6083[0:Res:6068.0,15.0] || -> para(skc6,skc7,skc7,skc6)*.
% 20.23/20.42 6095[0:Res:6083.0,14.0] || -> para(skc6,skc7,skc6,skc7)*.
% 20.23/20.42 6154[0:Res:5624.1,20.0] || coll(skc10,skc10,u) -> cyclic(u,skc11,skc10,skc10)*.
% 20.23/20.42 6200[0:Res:5667.1,2637.0] || coll(skc11,skc11,skc11) cyclic(skc11,skc10,skc11,skc10)* -> cong(skc11,skc10,skc11,skc10).
% 20.23/20.42 6202[0:MRR:6200.0,1431.0] || cyclic(skc11,skc10,skc11,skc10)* -> cong(skc11,skc10,skc11,skc10).
% 20.23/20.42 6251[0:Res:5911.1,616.0] || coll(skc10,skc10,u) -> para(skc10,u,skc10,u)*.
% 20.23/20.42 6271[0:Res:6056.1,19.0] || coll(skc7,skc7,u) -> cyclic(u,skc7,skc6,skc7)*.
% 20.23/20.42 6323[0:Res:6154.1,19.0] || coll(skc10,skc10,u) -> cyclic(u,skc10,skc11,skc10)*.
% 20.23/20.42 6601[0:Res:6271.1,2637.0] || coll(skc7,skc7,skc7) cyclic(skc7,skc7,skc6,skc7)* -> cong(skc7,skc7,skc7,skc7).
% 20.23/20.42 6602[0:MRR:6601.0,1261.0] || cyclic(skc7,skc7,skc6,skc7)* -> cong(skc7,skc7,skc7,skc7).
% 20.23/20.42 7581[0:Res:6251.1,14.0] || coll(skc10,skc10,u) -> para(skc10,u,u,skc10)*.
% 20.23/20.42 7724[0:Res:7581.1,15.0] || coll(skc10,skc10,u) -> para(u,skc10,skc10,u)*.
% 20.23/20.42 8172[0:Res:6323.1,6202.0] || coll(skc10,skc10,skc11) -> cong(skc11,skc10,skc11,skc10)*.
% 20.23/20.42 8176[0:MRR:8172.0,526.0] || -> cong(skc11,skc10,skc11,skc10)*.
% 20.23/20.42 8191[0:Res:8176.0,21.0] || -> cong(skc11,skc10,skc10,skc11)*.
% 20.23/20.42 8195[0:Res:8176.0,1425.0] || -> para(skc11,skc10,skc10,skc10)* perp(skc11,skc10,skc10,skc10).
% 20.23/20.42 8253[0:Res:8191.0,22.0] || -> cong(skc10,skc11,skc11,skc10)*.
% 20.23/20.42 8256[0:Res:8253.0,21.0] || -> cong(skc10,skc11,skc10,skc11)*.
% 20.23/20.42 8277[0:Res:8256.0,1425.0] || -> para(skc10,skc11,skc11,skc11)* perp(skc10,skc11,skc11,skc11).
% 20.23/20.42 8382[1:Spt:8195.0] || -> para(skc11,skc10,skc10,skc10)*.
% 20.23/20.42 8385[1:Res:8382.0,15.0] || -> para(skc10,skc10,skc11,skc10)*.
% 20.23/20.42 8396[1:Res:8385.0,14.0] || -> para(skc10,skc10,skc10,skc11)*.
% 20.23/20.42 8478[1:Res:8396.0,15.0] || -> para(skc10,skc11,skc10,skc10)*.
% 20.23/20.42 8485[1:Res:8396.0,87.1] || midp(u,skc10,skc10) para(skc10,skc11,skc10,skc10)* -> midp(u,skc11,skc10)*.
% 20.23/20.42 8488[1:MRR:8485.1,8478.0] || midp(u,skc10,skc10) -> midp(u,skc11,skc10)*.
% 20.23/20.42 8969[1:Res:8488.1,3341.0] || midp(skc7,skc10,skc10)* -> midp(skc6,skc10,skc11).
% 20.23/20.42 8972[1:Res:6017.1,8969.0] || midp(skc7,skc6,skc6)* -> midp(skc6,skc10,skc11).
% 20.23/20.42 14584[2:Spt:8277.0] || -> para(skc10,skc11,skc11,skc11)*.
% 20.23/20.42 14589[2:Res:14584.0,15.0] || -> para(skc11,skc11,skc10,skc11)*.
% 20.23/20.42 14611[2:Res:14589.0,14.0] || -> para(skc11,skc11,skc11,skc10)*.
% 20.23/20.42 14633[2:Res:14611.0,2631.0] || cyclic(skc11,u,skc11,skc10) cyclic(skc11,u,skc11,u)* cyclic(skc11,u,skc11,skc11)* -> cong(skc11,u,skc10,u).
% 20.23/20.42 14724[1:Res:8396.0,2633.0] || cyclic(skc10,skc10,skc10,skc11) cyclic(skc11,skc11,skc10,skc11)* cyclic(skc11,skc11,skc10,skc10) cyclic(skc11,skc11,skc10,skc10) -> cong(skc11,skc11,skc11,skc10).
% 20.23/20.42 14725[1:Obv:14724.2] || cyclic(skc10,skc10,skc10,skc11) cyclic(skc11,skc11,skc10,skc11)* cyclic(skc11,skc11,skc10,skc10) -> cong(skc11,skc11,skc11,skc10).
% 20.23/20.42 15182[0:Res:2844.1,12.0] || perp(skc11,skc10,u,skc7)* -> coll(skc7,skc6,u).
% 20.23/20.42 15909[0:Res:7724.1,4693.0] || coll(skc10,skc10,skc10) -> cyclic(skc10,skc10,skc10,u)*.
% 20.23/20.42 15920[0:Res:5715.0,4693.0] || -> cyclic(skc11,skc11,skc10,u)*.
% 20.23/20.42 15932[0:Res:6095.0,4693.0] || -> cyclic(skc7,skc7,skc6,u)*.
% 20.23/20.42 15959[1:MRR:14725.2,14725.1,15920.0] || cyclic(skc10,skc10,skc10,skc11)* -> cong(skc11,skc11,skc11,skc10).
% 20.23/20.42 15979[0:MRR:6602.0,15932.0] || -> cong(skc7,skc7,skc7,skc7)*.
% 20.23/20.42 16047[0:MRR:15909.0,894.0] || -> cyclic(skc10,skc10,skc10,u)*.
% 20.23/20.42 16076[1:MRR:15959.0,16047.0] || -> cong(skc11,skc11,skc11,skc10)*.
% 20.23/20.42 16348[0:Res:15979.0,38.1] || coll(skc7,skc7,skc7) -> midp(skc7,skc7,skc7)*.
% 20.23/20.42 16367[0:MRR:16348.0,1261.0] || -> midp(skc7,skc7,skc7)*.
% 20.23/20.42 16383[0:Res:16367.0,6080.0] || -> midp(skc7,skc6,skc6)*.
% 20.23/20.42 16384[1:MRR:8972.0,16383.0] || -> midp(skc6,skc10,skc11)*.
% 20.23/20.42 16426[1:MRR:3687.0,16384.0] || cong(skc11,u,skc10,u)* -> perp(skc11,skc10,u,skc7).
% 20.23/20.42 16813[1:Res:16076.0,38.1] || coll(skc11,skc11,skc10) -> midp(skc11,skc11,skc10)*.
% 20.23/20.42 16829[1:MRR:16813.0,533.0] || -> midp(skc11,skc11,skc10)*.
% 20.23/20.42 17389[0:Res:5671.0,5006.0] || -> para(u,v,u,v)*.
% 20.23/20.42 17422[0:MRR:1036.0,17389.0] || -> coll(u,u,v) cyclic(v,w,u,u)*.
% 20.23/20.42 17423[0:MRR:1368.0,17389.0] || coll(u,u,v) -> cyclic(w,v,u,u)*.
% 20.23/20.42 17425[0:MRR:4693.0,17389.0] || -> cyclic(u,u,v,w)*.
% 20.23/20.42 17622[0:Res:17422.1,20.0] || -> coll(u,u,v) cyclic(w,v,u,u)*.
% 20.23/20.42 17666[0:MRR:17622.0,17423.0] || -> cyclic(u,v,w,w)*.
% 20.23/20.42 17869[2:MRR:14633.2,17666.0] || cyclic(skc11,u,skc11,skc10)* cyclic(skc11,u,skc11,u)* -> cong(skc11,u,skc10,u).
% 20.23/20.42 19782[0:Res:17425.0,94.0] || cong(u,v,u,v)* cong(u,w,u,w)* -> perp(w,u,u,v)*.
% 20.23/20.42 19783[0:Res:17425.0,46.0] || cyclic(u,u,v,w)* -> cyclic(u,v,w,x)*.
% 20.23/20.42 19785[0:Res:17425.0,19.0] || -> cyclic(u,v,u,w)*.
% 20.23/20.42 19844[2:MRR:17869.0,17869.1,19785.0] || -> cong(skc11,u,skc10,u)*.
% 20.23/20.42 19904[2:MRR:16426.0,19844.0] || -> perp(skc11,skc10,u,skc7)*.
% 20.23/20.42 19989[2:MRR:15182.0,19904.0] || -> coll(skc7,skc6,u)*.
% 20.23/20.42 20110[0:MRR:19783.0,17425.0] || -> cyclic(u,v,w,x)*.
% 20.23/20.42 20130[0:MRR:2637.1,2637.0,20110.0] || -> cong(u,v,u,v)*.
% 20.23/20.42 20555[0:MRR:19782.0,19782.1,20130.0,20130.0] || -> perp(u,v,v,w)*.
% 20.23/20.42 20571[0:MRR:39.1,20555.0] || midp(u,v,w)*+ -> cong(v,u,x,u)*.
% 20.23/20.42 20830[2:Res:19989.0,25.0] || coll(skc7,skc6,u)* -> coll(u,v,skc7)*.
% 20.23/20.42 20903[2:MRR:20830.0,19989.0] || -> coll(u,v,skc7)*.
% 20.23/20.42 21024[2:Res:20903.0,8.0] || -> coll(u,skc7,v)*.
% 20.23/20.42 22407[0:Res:20130.0,38.1] || coll(u,v,v) -> midp(u,v,v)*.
% 20.23/20.42 22412[0:Res:20130.0,48.0] || cong(u,v,u,v)* -> perp(u,u,v,w)*.
% 20.23/20.42 22418[0:MRR:22412.0,20130.0] || -> perp(u,u,v,w)*.
% 20.23/20.42 22651[2:Res:21024.0,25.0] || coll(u,skc7,v)* -> coll(v,w,u)*.
% 20.23/20.42 22674[2:MRR:22651.0,21024.0] || -> coll(u,v,w)*.
% 20.23/20.42 22810[2:MRR:22407.0,22674.0] || -> midp(u,v,v)*.
% 20.23/20.42 23146[2:Res:22810.0,20571.0] || -> cong(u,v,w,v)*.
% 20.23/20.42 23152[2:MRR:48.1,48.0,23146.0] || -> perp(u,v,w,x)*.
% 20.23/20.42 23163[2:UnC:23152.0,7.0] || -> .
% 20.23/20.42 23167[2:Spt:23163.0,8277.0,14584.0] || para(skc10,skc11,skc11,skc11)* -> .
% 20.23/20.42 23168[2:Spt:23163.0,8277.1] || -> perp(skc10,skc11,skc11,skc11)*.
% 20.23/20.42 23556[2:Res:4311.1,23167.0] || midp(skc11,skc11,skc10)* -> .
% 20.23/20.42 23557[2:MRR:23556.0,16829.0] || -> .
% 20.23/20.42 23558[1:Spt:23557.0,8195.0,8382.0] || para(skc11,skc10,skc10,skc10)* -> .
% 20.23/20.42 23559[1:Spt:23557.0,8195.1] || -> perp(skc11,skc10,skc10,skc10)*.
% 20.46/20.67 23752[1:Res:2919.1,23558.0] || perp(skc10,skc10,skc7,skc6)* -> .
% 20.46/20.67 23753[1:MRR:23752.0,22418.0] || -> .
% 20.46/20.67 % SZS output end Refutation
% 20.46/20.67 Formulae used in the proof : exemplo6GDDFULL012006 ruleD1 ruleD2 ruleD66 ruleD68 ruleD4 ruleD5 ruleD7 ruleD8 ruleD15 ruleD16 ruleD23 ruleD24 ruleD3 ruleD39 ruleD40 ruleD41 ruleD46 ruleD67 ruleD52 ruleD55 ruleD9 ruleD17 ruleD56 ruleD19 ruleD21 ruleD42a ruleD72 ruleD42b ruleD64 ruleD54 ruleD57 ruleD43
% 20.46/20.67
%------------------------------------------------------------------------------