TSTP Solution File: GEO070-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GEO070-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 06:22:04 EDT 2022
% Result : Unsatisfiable 220.84s 220.97s
% Output : Refutation 222.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO070-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 06:46:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 220.84/220.97
% 220.84/220.97 SPASS V 3.9
% 220.84/220.97 SPASS beiseite: Proof found.
% 220.84/220.97 % SZS status Theorem
% 220.84/220.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 220.84/220.97 SPASS derived 63463 clauses, backtracked 15221 clauses, performed 12 splits and kept 38925 clauses.
% 220.84/220.97 SPASS allocated 114768 KBytes.
% 220.84/220.97 SPASS spent 0:3:40.53 on the problem.
% 220.84/220.97 0:00:00.04 for the input.
% 220.84/220.97 0:00:00.00 for the FLOTTER CNF translation.
% 220.84/220.97 0:00:00.73 for inferences.
% 220.84/220.97 0:00:06.98 for the backtracking.
% 220.84/220.97 0:3:31.84 for the reduction.
% 220.84/220.97
% 220.84/220.97
% 220.84/220.97 Here is a proof with depth 7, length 254 :
% 220.84/220.97 % SZS output start Refutation
% 220.84/220.97 2[0:Inp] || equidistant(u,v,w,x)*+ -> equidistant(w,x,u,v)*.
% 220.84/220.97 5[0:Inp] || equidistant(u,v,w,x)*+ -> equidistant(v,u,x,w)*.
% 220.84/220.97 6[0:Inp] || equidistant(u,v,w,x)*+ -> equidistant(w,x,v,u)*.
% 220.84/220.97 7[0:Inp] || equidistant(u,v,w,x)*+ -> equidistant(x,w,u,v)*.
% 220.84/220.97 8[0:Inp] || equidistant(u,v,w,x)*+ -> equidistant(x,w,v,u)*.
% 220.84/220.97 10[0:Inp] || -> equal(extension(u,v,w,w),v)**.
% 220.84/220.97 11[0:Inp] || equal(u,extension(v,w,x,y))*+ -> between(v,w,u)*.
% 220.84/220.97 13[0:Inp] || -> equidistant(u,reflection(v,u),v,u)*.
% 220.84/220.97 14[0:Inp] || equal(u,v) -> equal(reflection(u,v),v)**.
% 220.84/220.97 17[0:Inp] || -> equidistant(u,u,v,v)*.
% 220.84/220.97 20[0:Inp] || between(u,v,w) -> equal(u,v) equal(extension(u,v,v,w),w)**.
% 220.84/220.97 25[0:Inp] || -> between(u,v,v)*.
% 220.84/220.97 27[0:Inp] || between(u,v,w)*+ -> between(w,v,u)*.
% 220.84/220.97 28[0:Inp] || -> between(u,u,v)*.
% 220.84/220.97 29[0:Inp] || between(u,v,w)*+ between(v,u,w)* -> equal(v,u).
% 220.84/220.97 30[0:Inp] || between(u,v,w)*+ between(u,w,v)* -> equal(w,v).
% 220.84/220.97 35[0:Inp] || between(u,v,w)*+ between(x,u,v)* -> equal(u,v) between(x,v,w)*.
% 220.84/220.97 36[0:Inp] || between(u,v,w)*+ between(x,u,v)* -> equal(u,v) between(x,u,w)*.
% 220.84/220.97 37[0:Inp] || between(u,v,w)*+ between(x,u,w)* -> between(x,v,w)*.
% 220.84/220.97 48[0:Inp] || between(u,v,w)* between(x,y,z)* equidistant(x,z,u,w)*+ equidistant(x,y,u,v)* -> equidistant(y,z,v,w)*.
% 220.84/220.97 56[0:Inp] || between(u,v,w)* equidistant(u,w,x,y)*+ equidistant(v,w,z,y)* equidistant(u,v,x,z)* -> between(x,z,y)*.
% 220.84/220.97 58[0:Inp] || between(u,v,w)*+ between(u,v,x)* -> equal(u,v) between(v,w,x)* between(v,x,w)*.
% 220.84/220.97 60[0:Inp] || between(u,v,w)*+ between(u,x,w)* -> between(u,v,x)* between(u,x,v)*.
% 220.84/220.97 61[0:Inp] || between(u,v,w)*+ between(u,x,w)* -> between(v,x,w)* between(x,v,w)*.
% 220.84/220.97 62[0:Inp] || between(u,v,w)*+ between(x,y,v)* between(u,x,w)* -> between(u,y,w)*.
% 220.84/220.97 80[0:Inp] || colinear(u,v,w)*+ colinear(x,v,w)* -> equal(w,v) colinear(u,x,w)*.
% 220.84/220.97 83[0:Inp] || -> equidistant(u__dfg,v__dfg,w__dfg,x__dfg)*.
% 220.84/220.97 84[0:Inp] || -> equidistant(v__dfg,w__dfg,x__dfg,u__dfg)*.
% 220.84/220.97 85[0:Inp] || -> equidistant(u__dfg,w__dfg,v__dfg,x__dfg)*.
% 220.84/220.97 86[0:Inp] || -> between(u__dfg,y__dfg,w__dfg)*.
% 220.84/220.97 87[0:Inp] || -> between(v__dfg,y__dfg,x__dfg)*.
% 220.84/220.97 88[0:Inp] || equal(v__dfg,u__dfg)** -> .
% 220.84/220.97 89[0:Inp] || equal(x__dfg,u__dfg)** -> .
% 220.84/220.97 90[0:Inp] || -> colinear(u__dfg,v__dfg,w__dfg)*.
% 220.84/220.97 91[0:Inp] || -> equidistant(u,v,v,u)*.
% 220.84/220.97 92[0:Inp] || equidistant(u,v,w,x)*+ equidistant(u,v,y,z)* -> equidistant(y,z,w,x)*.
% 220.84/220.97 93[0:Inp] || equidistant(u,v,w,w)* -> equal(u,v).
% 220.84/220.97 94[0:Inp] || -> between(u,v,extension(u,v,w,x))*.
% 220.84/220.97 97[0:Inp] || between(u,v,u)* -> equal(u,v).
% 220.84/220.97 112[0:Inp] || colinear(u,v,w)* -> between(w,u,v) between(v,w,u) between(u,v,w).
% 220.84/220.97 122[0:Res:90.0,112.0] || -> between(w__dfg,u__dfg,v__dfg)* between(v__dfg,w__dfg,u__dfg) between(u__dfg,v__dfg,w__dfg).
% 220.84/220.97 133[0:Res:90.0,80.1] || colinear(u,v__dfg,w__dfg)*+ -> equal(w__dfg,v__dfg) colinear(u__dfg,u,w__dfg)*.
% 220.84/220.97 156[1:Spt:133.1] || -> equal(w__dfg,v__dfg)**.
% 220.84/220.97 166[1:Rew:156.0,84.0] || -> equidistant(v__dfg,v__dfg,x__dfg,u__dfg)*.
% 220.84/220.97 202[0:SpR:14.1,13.0] || equal(u,v) -> equidistant(v,v,u,v)*.
% 220.84/220.97 288[0:Res:94.0,27.0] || -> between(extension(u,v,w,x),v,u)*.
% 220.84/220.97 305[1:Res:166.0,8.0] || -> equidistant(u__dfg,x__dfg,v__dfg,v__dfg)*.
% 220.84/220.97 328[1:Res:305.0,93.0] || -> equal(x__dfg,u__dfg)**.
% 220.84/220.97 331[1:MRR:328.0,89.0] || -> .
% 220.84/220.97 332[1:Spt:331.0,133.1,156.0] || equal(w__dfg,v__dfg)** -> .
% 220.84/220.97 333[1:Spt:331.0,133.0,133.2] || colinear(u,v__dfg,w__dfg)*+ -> colinear(u__dfg,u,w__dfg)*.
% 220.84/220.97 348[0:Res:86.0,27.0] || -> between(w__dfg,y__dfg,u__dfg)*.
% 220.84/220.97 380[0:Res:83.0,7.0] || -> equidistant(x__dfg,w__dfg,u__dfg,v__dfg)*.
% 220.84/220.97 381[0:Res:83.0,8.0] || -> equidistant(x__dfg,w__dfg,v__dfg,u__dfg)*.
% 220.84/220.97 383[0:Res:84.0,7.0] || -> equidistant(u__dfg,x__dfg,v__dfg,w__dfg)*.
% 220.84/220.97 384[0:Res:84.0,8.0] || -> equidistant(u__dfg,x__dfg,w__dfg,v__dfg)*.
% 220.84/220.97 385[0:Res:85.0,7.0] || -> equidistant(x__dfg,v__dfg,u__dfg,w__dfg)*.
% 220.84/220.97 386[0:Res:85.0,8.0] || -> equidistant(x__dfg,v__dfg,w__dfg,u__dfg)*.
% 220.84/220.97 387[0:Res:380.0,7.0] || -> equidistant(v__dfg,u__dfg,x__dfg,w__dfg)*.
% 220.84/220.97 400[0:Res:85.0,6.0] || -> equidistant(v__dfg,x__dfg,w__dfg,u__dfg)*.
% 220.84/220.97 403[0:Res:381.0,7.0] || -> equidistant(u__dfg,v__dfg,x__dfg,w__dfg)*.
% 220.84/220.97 406[0:Res:383.0,7.0] || -> equidistant(w__dfg,v__dfg,u__dfg,x__dfg)*.
% 220.84/220.97 409[0:Res:384.0,7.0] || -> equidistant(v__dfg,w__dfg,u__dfg,x__dfg)*.
% 220.84/220.97 412[0:Res:385.0,7.0] || -> equidistant(w__dfg,u__dfg,x__dfg,v__dfg)*.
% 220.84/220.97 413[0:Res:385.0,8.0] || -> equidistant(w__dfg,u__dfg,v__dfg,x__dfg)*.
% 220.84/220.97 679[0:SpL:10.0,11.0] || equal(u,v) -> between(w,v,u)*.
% 220.84/220.97 716[0:Res:679.1,27.0] || equal(u,v) -> between(u,v,w)*.
% 220.84/220.97 743[0:Res:86.0,30.0] || between(u__dfg,w__dfg,y__dfg)* -> equal(y__dfg,w__dfg).
% 220.84/220.97 767[0:Res:716.1,743.0] || equal(w__dfg,u__dfg) -> equal(y__dfg,w__dfg)**.
% 220.84/220.97 782[0:SpR:767.1,87.0] || equal(w__dfg,u__dfg) -> between(v__dfg,w__dfg,x__dfg)*.
% 220.84/220.97 927[0:Res:86.0,37.0] || between(u,u__dfg,w__dfg) -> between(u,y__dfg,w__dfg)*.
% 220.84/220.97 1510[0:Res:87.0,36.0] || between(u,v__dfg,y__dfg)* -> equal(y__dfg,v__dfg) between(u,v__dfg,x__dfg).
% 220.84/220.97 1512[0:Res:86.0,36.0] || between(u,u__dfg,y__dfg)* -> equal(y__dfg,u__dfg) between(u,u__dfg,w__dfg).
% 220.84/220.97 1590[0:Res:87.0,35.0] || between(u,v__dfg,y__dfg) -> equal(y__dfg,v__dfg) between(u,y__dfg,x__dfg)*.
% 220.84/220.97 1834[0:Res:17.0,92.0] || equidistant(u,u,v,w)*+ -> equidistant(v,w,x,x)*.
% 220.84/220.97 1990[0:Res:87.0,61.0] || between(v__dfg,u,x__dfg)+ -> between(y__dfg,u,x__dfg)* between(u,y__dfg,x__dfg)*.
% 220.84/220.97 1992[0:Res:86.0,61.0] || between(u__dfg,u,w__dfg)+ -> between(y__dfg,u,w__dfg)* between(u,y__dfg,w__dfg)*.
% 220.84/220.97 2073[0:Res:87.0,60.0] || between(v__dfg,u,x__dfg)+ -> between(v__dfg,y__dfg,u)* between(v__dfg,u,y__dfg)*.
% 220.84/220.97 2162[0:Res:87.0,62.0] || between(u,v,y__dfg)*+ between(v__dfg,u,x__dfg)* -> between(v__dfg,v,x__dfg)*.
% 220.84/220.97 2164[0:Res:86.0,62.0] || between(u,v,y__dfg)*+ between(u__dfg,u,w__dfg)* -> between(u__dfg,v,w__dfg)*.
% 220.84/220.97 2889[0:Res:87.0,58.0] || between(v__dfg,y__dfg,u) -> equal(y__dfg,v__dfg) between(y__dfg,x__dfg,u)* between(y__dfg,u,x__dfg)*.
% 220.84/220.97 3514[0:Res:83.0,48.2] || between(w__dfg,u,x__dfg) between(u__dfg,v,v__dfg) equidistant(u__dfg,v,w__dfg,u)*+ -> equidistant(v,v__dfg,u,x__dfg)*.
% 220.84/220.97 3520[0:Res:85.0,48.2] || between(v__dfg,u,x__dfg) between(u__dfg,v,w__dfg) equidistant(u__dfg,v,v__dfg,u)*+ -> equidistant(v,w__dfg,u,x__dfg)*.
% 220.84/220.97 3815[0:Res:91.0,56.1] || between(u,v,w) equidistant(v,w,x,u)*+ equidistant(u,v,w,x)* -> between(w,x,u).
% 220.84/220.97 3817[0:Res:17.0,56.1] || between(u,v,u)* equidistant(v,u,w,x)* equidistant(u,v,x,w)* -> between(x,w,x)*.
% 220.84/220.97 3830[0:Res:83.0,56.1] || between(u__dfg,u,v__dfg) equidistant(u,v__dfg,v,x__dfg)*+ equidistant(u__dfg,u,w__dfg,v)* -> between(w__dfg,v,x__dfg).
% 220.84/220.97 3834[0:Res:84.0,56.1] || between(v__dfg,u,w__dfg) equidistant(u,w__dfg,v,u__dfg)*+ equidistant(v__dfg,u,x__dfg,v)* -> between(x__dfg,v,u__dfg).
% 220.84/220.97 3836[0:Res:85.0,56.1] || between(u__dfg,u,w__dfg) equidistant(u,w__dfg,v,x__dfg)*+ equidistant(u__dfg,u,v__dfg,v)* -> between(v__dfg,v,x__dfg).
% 220.84/220.97 3856[0:MRR:3817.1,5.1] || between(u,v,u)* equidistant(u,v,w,x)*+ -> between(w,x,w)*.
% 220.84/220.97 8069[0:Res:202.1,1834.0] || equal(u,v) -> equidistant(u,v,w,w)*.
% 220.84/220.97 8422[2:Spt:1510.1] || -> equal(y__dfg,v__dfg)**.
% 220.84/220.97 8425[2:Rew:8422.0,86.0] || -> between(u__dfg,v__dfg,w__dfg)*.
% 220.84/220.97 8426[2:Rew:8422.0,348.0] || -> between(w__dfg,v__dfg,u__dfg)*.
% 220.84/220.97 8593[2:Rew:8422.0,1512.0] || between(u,u__dfg,v__dfg) -> equal(y__dfg,u__dfg) between(u,u__dfg,w__dfg)*.
% 220.84/220.97 9214[2:Rew:8422.0,8593.1] || between(u,u__dfg,v__dfg) -> equal(v__dfg,u__dfg) between(u,u__dfg,w__dfg)*.
% 220.84/220.97 9215[2:MRR:9214.1,88.0] || between(u,u__dfg,v__dfg) -> between(u,u__dfg,w__dfg)*.
% 220.84/220.97 9791[2:Res:9215.1,27.0] || between(u,u__dfg,v__dfg)*+ -> between(w__dfg,u__dfg,u)*.
% 220.84/220.97 11923[2:Res:288.0,9791.0] || -> between(w__dfg,u__dfg,extension(v__dfg,u__dfg,u,v))*.
% 220.84/220.97 11993[2:Res:11923.0,27.0] || -> between(extension(v__dfg,u__dfg,u,v),u__dfg,w__dfg)*.
% 220.84/220.97 12004[2:SpR:20.2,11993.0] || between(v__dfg,u__dfg,u)* -> equal(v__dfg,u__dfg) between(u,u__dfg,w__dfg)*.
% 220.84/220.97 12022[2:MRR:12004.1,88.0] || between(v__dfg,u__dfg,u)*+ -> between(u,u__dfg,w__dfg)*.
% 220.84/220.97 14002[0:Res:383.0,3856.1] || between(u__dfg,x__dfg,u__dfg) -> between(v__dfg,w__dfg,v__dfg)*.
% 220.84/220.97 14007[0:Res:409.0,3856.1] || between(v__dfg,w__dfg,v__dfg)* -> between(u__dfg,x__dfg,u__dfg).
% 220.84/220.97 15345[0:Res:14002.1,97.0] || between(u__dfg,x__dfg,u__dfg)* -> equal(w__dfg,v__dfg).
% 220.84/220.97 15371[1:MRR:15345.1,332.0] || between(u__dfg,x__dfg,u__dfg)* -> .
% 220.84/220.97 15372[1:MRR:14007.1,15371.0] || between(v__dfg,w__dfg,v__dfg)* -> .
% 220.84/220.97 24993[0:Res:8069.1,2.0] || equal(u,v) -> equidistant(w,w,u,v)*.
% 220.84/220.97 25440[0:Res:8069.1,3520.2] || equal(u__dfg,u) between(v__dfg,v__dfg,x__dfg) between(u__dfg,u,w__dfg) -> equidistant(u,w__dfg,v__dfg,x__dfg)*.
% 220.84/220.97 25455[0:Res:24993.1,3520.2] || equal(v__dfg,u) between(v__dfg,u,x__dfg) between(u__dfg,u__dfg,w__dfg) -> equidistant(u__dfg,w__dfg,u,x__dfg)*.
% 220.84/220.97 25468[0:MRR:25440.1,25440.2,28.0,716.1] || equal(u__dfg,u) -> equidistant(u,w__dfg,v__dfg,x__dfg)*.
% 220.84/220.97 25470[0:MRR:25455.1,25455.2,716.1,28.0] || equal(v__dfg,u) -> equidistant(u__dfg,w__dfg,u,x__dfg)*.
% 220.84/220.97 25487[0:Res:25468.1,2.0] || equal(u__dfg,u) -> equidistant(v__dfg,x__dfg,u,w__dfg)*.
% 220.84/220.97 25517[0:Res:25470.1,93.0] || equal(x__dfg,v__dfg)** -> equal(w__dfg,u__dfg).
% 220.84/220.97 25548[0:Res:25487.1,93.0] || equal(w__dfg,u__dfg) -> equal(x__dfg,v__dfg)**.
% 220.84/220.97 25757[0:Res:24993.1,3514.2] || equal(w__dfg,u) between(w__dfg,u,x__dfg) between(u__dfg,u__dfg,v__dfg) -> equidistant(u__dfg,v__dfg,u,x__dfg)*.
% 220.84/220.97 25772[0:MRR:25757.1,25757.2,716.1,28.0] || equal(w__dfg,u) -> equidistant(u__dfg,v__dfg,u,x__dfg)*.
% 220.84/220.97 26316[0:Res:25772.1,93.0] || equal(x__dfg,w__dfg)** -> equal(v__dfg,u__dfg).
% 220.84/220.97 26824[0:Res:91.0,3836.1] || between(u__dfg,x__dfg,w__dfg) equidistant(u__dfg,x__dfg,v__dfg,w__dfg)* -> between(v__dfg,w__dfg,x__dfg).
% 220.84/220.97 26832[0:Res:409.0,3836.1] || between(u__dfg,v__dfg,w__dfg) equidistant(u__dfg,v__dfg,v__dfg,u__dfg)* -> between(v__dfg,u__dfg,x__dfg).
% 220.84/220.97 26866[0:MRR:26824.1,383.0] || between(u__dfg,x__dfg,w__dfg) -> between(v__dfg,w__dfg,x__dfg)*.
% 220.84/220.97 26867[2:MRR:26832.0,26832.1,8425.0,91.0] || -> between(v__dfg,u__dfg,x__dfg)*.
% 220.84/220.97 26984[0:Res:381.0,3834.1] || between(v__dfg,x__dfg,w__dfg) equidistant(v__dfg,x__dfg,x__dfg,v__dfg)* -> between(x__dfg,v__dfg,u__dfg).
% 220.84/220.97 27011[0:MRR:26984.1,91.0] || between(v__dfg,x__dfg,w__dfg) -> between(x__dfg,v__dfg,u__dfg)*.
% 220.84/220.97 27114[2:Res:26867.0,12022.0] || -> between(x__dfg,u__dfg,w__dfg)*.
% 220.84/220.97 27195[0:Res:406.0,3830.1] || between(u__dfg,w__dfg,v__dfg) equidistant(u__dfg,w__dfg,w__dfg,u__dfg)* -> between(w__dfg,u__dfg,x__dfg).
% 220.84/220.97 27270[2:Res:27114.0,29.0] || between(u__dfg,x__dfg,w__dfg)* -> equal(x__dfg,u__dfg).
% 220.84/220.97 27274[2:MRR:27270.1,89.0] || between(u__dfg,x__dfg,w__dfg)* -> .
% 220.84/220.97 29488[0:Res:403.0,3815.1] || between(w__dfg,u__dfg,v__dfg) equidistant(w__dfg,u__dfg,v__dfg,x__dfg)* -> between(v__dfg,x__dfg,w__dfg).
% 220.84/220.97 29489[0:Res:383.0,3815.1] || between(w__dfg,u__dfg,x__dfg) equidistant(w__dfg,u__dfg,x__dfg,v__dfg)* -> between(x__dfg,v__dfg,w__dfg).
% 220.84/220.97 29491[0:Res:84.0,3815.1] || between(u__dfg,v__dfg,w__dfg) equidistant(u__dfg,v__dfg,w__dfg,x__dfg)* -> between(w__dfg,x__dfg,u__dfg).
% 220.84/220.97 29498[0:Res:409.0,3815.1] || between(x__dfg,v__dfg,w__dfg) equidistant(x__dfg,v__dfg,w__dfg,u__dfg)* -> between(w__dfg,u__dfg,x__dfg).
% 220.84/220.97 29501[0:Res:380.0,3815.1] || between(v__dfg,x__dfg,w__dfg) equidistant(v__dfg,x__dfg,w__dfg,u__dfg)* -> between(w__dfg,u__dfg,v__dfg).
% 220.84/220.97 29504[0:Res:381.0,3815.1] || between(u__dfg,x__dfg,w__dfg) equidistant(u__dfg,x__dfg,w__dfg,v__dfg)* -> between(w__dfg,v__dfg,u__dfg).
% 220.84/220.97 29542[0:Res:387.0,3815.1] || between(w__dfg,v__dfg,u__dfg) equidistant(w__dfg,v__dfg,u__dfg,x__dfg)* -> between(u__dfg,x__dfg,w__dfg).
% 220.84/220.97 29550[0:Res:412.0,3815.1] || between(v__dfg,w__dfg,u__dfg) equidistant(v__dfg,w__dfg,u__dfg,x__dfg)* -> between(u__dfg,x__dfg,v__dfg).
% 220.84/220.97 29551[0:Res:413.0,3815.1] || between(x__dfg,w__dfg,u__dfg) equidistant(x__dfg,w__dfg,u__dfg,v__dfg)* -> between(u__dfg,v__dfg,x__dfg).
% 220.84/220.97 29691[2:MRR:29542.0,29542.1,29542.2,8426.0,406.0,27274.0] || -> .
% 220.84/220.97 29736[2:Spt:29691.0,1510.1,8422.0] || equal(y__dfg,v__dfg)** -> .
% 220.84/220.97 29737[2:Spt:29691.0,1510.0,1510.2] || between(u,v__dfg,y__dfg)* -> between(u,v__dfg,x__dfg).
% 220.84/220.97 29738[0:MRR:26316.1,88.0] || equal(x__dfg,w__dfg)** -> .
% 220.84/220.97 29742[0:Rew:25548.1,782.1] || equal(w__dfg,u__dfg) -> between(v__dfg,w__dfg,v__dfg)*.
% 220.84/220.97 29743[1:MRR:29742.1,15372.0] || equal(w__dfg,u__dfg)** -> .
% 220.84/220.97 29744[1:MRR:25517.1,29743.0] || equal(x__dfg,v__dfg)** -> .
% 220.84/220.97 29775[2:MRR:1590.1,29736.0] || between(u,v__dfg,y__dfg) -> between(u,y__dfg,x__dfg)*.
% 220.84/220.97 29881[0:MRR:26832.1,91.0] || between(u__dfg,v__dfg,w__dfg) -> between(v__dfg,u__dfg,x__dfg)*.
% 220.84/220.97 29884[0:MRR:27195.1,91.0] || between(u__dfg,w__dfg,v__dfg) -> between(w__dfg,u__dfg,x__dfg)*.
% 220.84/220.97 29886[0:MRR:29488.1,413.0] || between(w__dfg,u__dfg,v__dfg)* -> between(v__dfg,x__dfg,w__dfg).
% 220.84/220.97 29887[0:MRR:29489.1,412.0] || between(w__dfg,u__dfg,x__dfg) -> between(x__dfg,v__dfg,w__dfg)*.
% 220.84/220.97 29889[0:MRR:29491.1,83.0] || between(u__dfg,v__dfg,w__dfg) -> between(w__dfg,x__dfg,u__dfg)*.
% 220.84/220.97 29892[0:MRR:29498.1,386.0] || between(x__dfg,v__dfg,w__dfg)* -> between(w__dfg,u__dfg,x__dfg).
% 220.84/220.97 29893[0:MRR:29501.1,400.0] || between(v__dfg,x__dfg,w__dfg) -> between(w__dfg,u__dfg,v__dfg)*.
% 220.84/220.97 29894[0:MRR:29504.1,384.0] || between(u__dfg,x__dfg,w__dfg) -> between(w__dfg,v__dfg,u__dfg)*.
% 220.84/220.97 29899[0:MRR:29542.1,406.0] || between(w__dfg,v__dfg,u__dfg)* -> between(u__dfg,x__dfg,w__dfg).
% 220.84/220.97 29902[0:MRR:29550.1,409.0] || between(v__dfg,w__dfg,u__dfg)* -> between(u__dfg,x__dfg,v__dfg).
% 220.84/220.97 29903[0:MRR:29551.1,380.0] || between(x__dfg,w__dfg,u__dfg)* -> between(u__dfg,v__dfg,x__dfg).
% 220.84/220.97 29912[2:MRR:2889.1,29736.0] || between(v__dfg,y__dfg,u)+ -> between(y__dfg,x__dfg,u)* between(y__dfg,u,x__dfg)*.
% 220.84/220.97 31707[2:Res:29775.1,30.0] || between(u,v__dfg,y__dfg) between(u,x__dfg,y__dfg)* -> equal(y__dfg,x__dfg).
% 220.84/220.97 31729[3:Spt:122.0] || -> between(w__dfg,u__dfg,v__dfg)*.
% 220.84/220.97 31730[3:MRR:29886.0,31729.0] || -> between(v__dfg,x__dfg,w__dfg)*.
% 220.84/220.97 31732[3:MRR:27011.0,31730.0] || -> between(x__dfg,v__dfg,u__dfg)*.
% 220.84/220.97 31802[3:Res:31729.0,30.0] || between(w__dfg,v__dfg,u__dfg)* -> equal(v__dfg,u__dfg).
% 220.84/220.97 31803[3:Res:31729.0,27.0] || -> between(v__dfg,u__dfg,w__dfg)*.
% 220.84/220.97 31839[3:MRR:31802.1,88.0] || between(w__dfg,v__dfg,u__dfg)* -> .
% 220.84/220.97 31840[3:MRR:29894.1,31839.0] || between(u__dfg,x__dfg,w__dfg)* -> .
% 220.84/220.97 31891[3:Res:31730.0,30.0] || between(v__dfg,w__dfg,x__dfg)* -> equal(x__dfg,w__dfg).
% 220.84/220.97 31899[3:MRR:31891.1,29738.0] || between(v__dfg,w__dfg,x__dfg)* -> .
% 220.84/220.97 31955[3:Res:31732.0,37.0] || between(u,x__dfg,u__dfg)* -> between(u,v__dfg,u__dfg).
% 220.84/220.97 32076[4:Spt:1512.1] || -> equal(y__dfg,u__dfg)**.
% 220.84/220.97 32178[4:Rew:32076.0,31707.2] || between(u,v__dfg,y__dfg) between(u,x__dfg,y__dfg)* -> equal(x__dfg,u__dfg).
% 220.84/220.97 33132[4:Rew:32076.0,32178.1,32076.0,32178.0] || between(u,v__dfg,u__dfg) between(u,x__dfg,u__dfg)* -> equal(x__dfg,u__dfg).
% 220.84/220.97 33133[4:MRR:33132.2,89.0] || between(u,v__dfg,u__dfg) between(u,x__dfg,u__dfg)* -> .
% 220.84/220.97 33134[4:MRR:33133.0,31955.1] || between(u,x__dfg,u__dfg)* -> .
% 220.84/220.97 33135[4:UnC:33134.0,288.0] || -> .
% 220.84/220.97 33651[4:Spt:33135.0,1512.1,32076.0] || equal(y__dfg,u__dfg)** -> .
% 220.84/220.97 33652[4:Spt:33135.0,1512.0,1512.2] || between(u,u__dfg,y__dfg)* -> between(u,u__dfg,w__dfg).
% 220.84/220.97 34019[0:Res:86.0,36.0] || between(u,u__dfg,y__dfg)* -> equal(y__dfg,u__dfg) between(u,u__dfg,w__dfg).
% 220.84/220.97 35081[2:Res:927.1,29912.0] || between(v__dfg,u__dfg,w__dfg) -> between(y__dfg,x__dfg,w__dfg)* between(y__dfg,w__dfg,x__dfg).
% 220.84/220.97 35086[3:MRR:35081.0,31803.0] || -> between(y__dfg,x__dfg,w__dfg)* between(y__dfg,w__dfg,x__dfg).
% 220.84/220.97 35232[3:Res:35086.0,27.0] || -> between(y__dfg,w__dfg,x__dfg)* between(w__dfg,x__dfg,y__dfg).
% 220.84/220.97 35289[5:Spt:35232.0] || -> between(y__dfg,w__dfg,x__dfg)*.
% 220.84/220.97 35332[5:Res:35289.0,27.0] || -> between(x__dfg,w__dfg,y__dfg)*.
% 220.84/220.97 35525[5:Res:35332.0,2162.0] || between(v__dfg,x__dfg,x__dfg)* -> between(v__dfg,w__dfg,x__dfg).
% 220.84/220.97 35528[5:MRR:35525.0,35525.1,25.0,31899.0] || -> .
% 220.84/220.97 35529[5:Spt:35528.0,35232.0,35289.0] || between(y__dfg,w__dfg,x__dfg)* -> .
% 220.84/220.97 35530[5:Spt:35528.0,35232.1] || -> between(w__dfg,x__dfg,y__dfg)*.
% 220.84/220.97 35806[5:Res:35530.0,2164.0] || between(u__dfg,w__dfg,w__dfg) -> between(u__dfg,x__dfg,w__dfg)*.
% 220.84/220.97 35807[5:MRR:35806.0,35806.1,25.0,31840.0] || -> .
% 220.84/220.97 35808[3:Spt:35807.0,122.0,31729.0] || between(w__dfg,u__dfg,v__dfg)* -> .
% 220.84/220.97 35809[3:Spt:35807.0,122.1,122.2] || -> between(v__dfg,w__dfg,u__dfg)* between(u__dfg,v__dfg,w__dfg).
% 220.84/220.97 35810[3:MRR:29893.1,35808.0] || between(v__dfg,x__dfg,w__dfg)* -> .
% 222.03/222.16 35815[4:Spt:35809.0] || -> between(v__dfg,w__dfg,u__dfg)*.
% 222.03/222.16 35816[4:MRR:29902.0,35815.0] || -> between(u__dfg,x__dfg,v__dfg)*.
% 222.03/222.16 35875[4:Res:35815.0,35.0] || between(u,v__dfg,w__dfg) -> equal(w__dfg,v__dfg) between(u,w__dfg,u__dfg)*.
% 222.03/222.16 35882[4:Res:35815.0,27.0] || -> between(u__dfg,w__dfg,v__dfg)*.
% 222.03/222.16 35883[4:MRR:29884.0,35882.0] || -> between(w__dfg,u__dfg,x__dfg)*.
% 222.03/222.16 35886[4:MRR:29887.0,35883.0] || -> between(x__dfg,v__dfg,w__dfg)*.
% 222.03/222.16 35912[4:MRR:35875.1,332.0] || between(u,v__dfg,w__dfg) -> between(u,w__dfg,u__dfg)*.
% 222.03/222.16 35962[4:Res:35816.0,30.0] || between(u__dfg,v__dfg,x__dfg)* -> equal(x__dfg,v__dfg).
% 222.03/222.16 35974[4:MRR:35962.1,29744.0] || between(u__dfg,v__dfg,x__dfg)* -> .
% 222.03/222.16 35975[4:MRR:29903.1,35974.0] || between(x__dfg,w__dfg,u__dfg)* -> .
% 222.03/222.16 63410[4:Res:35912.1,35975.0] || between(x__dfg,v__dfg,w__dfg)* -> .
% 222.03/222.16 63414[4:MRR:63410.0,35886.0] || -> .
% 222.03/222.16 63418[4:Spt:63414.0,35809.0,35815.0] || between(v__dfg,w__dfg,u__dfg)* -> .
% 222.03/222.16 63419[4:Spt:63414.0,35809.1] || -> between(u__dfg,v__dfg,w__dfg)*.
% 222.03/222.16 63421[4:MRR:29881.0,63419.0] || -> between(v__dfg,u__dfg,x__dfg)*.
% 222.03/222.16 63422[4:MRR:29889.0,63419.0] || -> between(w__dfg,x__dfg,u__dfg)*.
% 222.03/222.16 63553[4:Res:63419.0,27.0] || -> between(w__dfg,v__dfg,u__dfg)*.
% 222.03/222.16 63554[4:Res:63419.0,1992.0] || -> between(y__dfg,v__dfg,w__dfg)* between(v__dfg,y__dfg,w__dfg).
% 222.03/222.16 63556[4:MRR:29899.0,63553.0] || -> between(u__dfg,x__dfg,w__dfg)*.
% 222.03/222.16 63562[4:MRR:26866.0,63556.0] || -> between(v__dfg,w__dfg,x__dfg)*.
% 222.03/222.16 63656[4:Res:63421.0,1990.0] || -> between(y__dfg,u__dfg,x__dfg)* between(u__dfg,y__dfg,x__dfg).
% 222.03/222.16 63720[4:Res:63422.0,30.0] || between(w__dfg,u__dfg,x__dfg)* -> equal(x__dfg,u__dfg).
% 222.03/222.16 63722[4:MRR:63720.1,89.0] || between(w__dfg,u__dfg,x__dfg)* -> .
% 222.03/222.16 63723[4:MRR:29892.1,63722.0] || between(x__dfg,v__dfg,w__dfg)* -> .
% 222.03/222.16 63912[4:Res:63556.0,30.0] || between(u__dfg,w__dfg,x__dfg)* -> equal(x__dfg,w__dfg).
% 222.03/222.16 63914[4:Res:63556.0,1992.0] || -> between(y__dfg,x__dfg,w__dfg)* between(x__dfg,y__dfg,w__dfg).
% 222.03/222.16 63926[4:MRR:63912.1,29738.0] || between(u__dfg,w__dfg,x__dfg)* -> .
% 222.03/222.16 63993[4:Res:63562.0,2073.0] || -> between(v__dfg,y__dfg,w__dfg)* between(v__dfg,w__dfg,y__dfg).
% 222.03/222.16 63994[4:Res:63562.0,1990.0] || -> between(y__dfg,w__dfg,x__dfg)* between(w__dfg,y__dfg,x__dfg).
% 222.03/222.16 64108[5:Spt:34019.1] || -> equal(y__dfg,u__dfg)**.
% 222.03/222.16 65826[5:Rew:64108.0,63994.0] || -> between(u__dfg,w__dfg,x__dfg) between(w__dfg,y__dfg,x__dfg)*.
% 222.03/222.16 65845[5:Rew:64108.0,65826.1] || -> between(u__dfg,w__dfg,x__dfg) between(w__dfg,u__dfg,x__dfg)*.
% 222.03/222.16 65846[5:MRR:65845.1,63722.0] || -> between(u__dfg,w__dfg,x__dfg)*.
% 222.03/222.16 65847[5:MRR:65846.0,63926.0] || -> .
% 222.03/222.16 66957[5:Spt:65847.0,34019.1,64108.0] || equal(y__dfg,u__dfg)** -> .
% 222.03/222.16 66958[5:Spt:65847.0,34019.0,34019.2] || between(u,u__dfg,y__dfg)* -> between(u,u__dfg,w__dfg).
% 222.03/222.16 68534[4:Res:63994.0,30.0] || between(y__dfg,x__dfg,w__dfg)* -> between(w__dfg,y__dfg,x__dfg) equal(x__dfg,w__dfg).
% 222.03/222.16 68536[4:MRR:68534.2,29738.0] || between(y__dfg,x__dfg,w__dfg)* -> between(w__dfg,y__dfg,x__dfg).
% 222.03/222.16 68569[6:Spt:63914.0] || -> between(y__dfg,x__dfg,w__dfg)*.
% 222.03/222.16 68570[6:MRR:68536.0,68569.0] || -> between(w__dfg,y__dfg,x__dfg)*.
% 222.03/222.16 68619[6:Res:68569.0,29.0] || between(x__dfg,y__dfg,w__dfg)* -> equal(y__dfg,x__dfg).
% 222.03/222.16 68674[6:Res:68570.0,27.0] || -> between(x__dfg,y__dfg,w__dfg)*.
% 222.03/222.16 68675[6:MRR:68619.0,68674.0] || -> equal(y__dfg,x__dfg)**.
% 222.03/222.16 69292[6:Rew:68675.0,63554.1] || -> between(y__dfg,v__dfg,w__dfg)* between(v__dfg,x__dfg,w__dfg).
% 222.03/222.16 70557[6:Rew:68675.0,69292.0] || -> between(x__dfg,v__dfg,w__dfg)* between(v__dfg,x__dfg,w__dfg).
% 222.03/222.16 70558[6:MRR:70557.0,70557.1,63723.0,35810.0] || -> .
% 222.03/222.16 71744[6:Spt:70558.0,63914.0,68569.0] || between(y__dfg,x__dfg,w__dfg)* -> .
% 222.03/222.16 71745[6:Spt:70558.0,63914.1] || -> between(x__dfg,y__dfg,w__dfg)*.
% 222.03/222.16 71807[6:Res:71745.0,27.0] || -> between(w__dfg,y__dfg,x__dfg)*.
% 222.03/222.16 72060[6:Res:71807.0,29.0] || between(y__dfg,w__dfg,x__dfg)* -> equal(y__dfg,w__dfg).
% 222.03/222.16 73549[7:Spt:63554.1] || -> between(v__dfg,y__dfg,w__dfg)*.
% 222.03/222.16 73601[7:Res:73549.0,29912.0] || -> between(y__dfg,x__dfg,w__dfg)* between(y__dfg,w__dfg,x__dfg).
% 222.03/222.16 73604[7:MRR:73601.0,71744.0] || -> between(y__dfg,w__dfg,x__dfg)*.
% 222.03/222.16 73605[7:MRR:72060.0,73604.0] || -> equal(y__dfg,w__dfg)**.
% 222.03/222.16 73823[7:Rew:73605.0,63656.1] || -> between(y__dfg,u__dfg,x__dfg)* between(u__dfg,w__dfg,x__dfg).
% 222.03/222.16 75535[7:Rew:73605.0,73823.0] || -> between(w__dfg,u__dfg,x__dfg)* between(u__dfg,w__dfg,x__dfg).
% 222.03/222.16 75536[7:MRR:75535.0,75535.1,63722.0,63926.0] || -> .
% 222.03/222.16 76612[7:Spt:75536.0,63554.1,73549.0] || between(v__dfg,y__dfg,w__dfg)* -> .
% 222.03/222.16 76613[7:Spt:75536.0,63554.0] || -> between(y__dfg,v__dfg,w__dfg)*.
% 222.03/222.16 76614[7:MRR:63993.0,76612.0] || -> between(v__dfg,w__dfg,y__dfg)*.
% 222.03/222.16 76673[7:Res:76613.0,27.0] || -> between(w__dfg,v__dfg,y__dfg)*.
% 222.03/222.16 77038[7:Res:76614.0,29.0] || between(w__dfg,v__dfg,y__dfg)* -> equal(w__dfg,v__dfg).
% 222.03/222.16 77042[7:MRR:77038.1,332.0] || between(w__dfg,v__dfg,y__dfg)* -> .
% 222.03/222.16 77043[7:MRR:77042.0,76673.0] || -> .
% 222.03/222.16 % SZS output end Refutation
% 222.03/222.16 Formulae used in the proof : d2 d4_2 d4_3 d4_4 d4_5 e1 b0 r2_2 r3_1 d7 d10_1 t3 t1 t2 b2 b3 b6 b7 b8 d13 b11 b13 t9 b14 t8 c5_1 u_to_v_equals_w_to_x v_to_w_equals_x_to_u u_to_w_equals_v_to_x y_between_u_and_w y_between_v_and_x u_not_v x_not_u prove_uvw_not_colinear reflexivity_for_equidistance transitivity_for_equidistance identity_for_equidistance segment_construction1 identity_for_betweeness colinearity4
% 222.03/222.16
%------------------------------------------------------------------------------