TSTP Solution File: GRP731-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP731-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:49:12 EDT 2022
% Result : Unsatisfiable 23.64s 23.82s
% Output : Refutation 23.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 96 RR)
% Number of literals : 96 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(unit,u),u),
file('GRP731-1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(u,unit),u),
file('GRP731-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,i(u)),unit),
file('GRP731-1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(i(u),u),unit),
file('GRP731-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(i(u),i(v)),i(mult(u,v))),
file('GRP731-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(i(u),mult(u,v)),v),
file('GRP731-1.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(u,v),v),u),
file('GRP731-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(rd(u,v),v),u),
file('GRP731-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))),
file('GRP731-1.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(mult(u,mult(v,w)),asoc(u,v,w)),mult(mult(u,v),w)),
file('GRP731-1.p',unknown),
[] ).
cnf(11,axiom,
equal(mult(mult(u,v),op_k(v,u)),mult(v,u)),
file('GRP731-1.p',unknown),
[] ).
cnf(12,axiom,
equal(mult(i(mult(u,v)),mult(u,mult(v,w))),op_l(w,v,u)),
file('GRP731-1.p',unknown),
[] ).
cnf(14,axiom,
equal(mult(i(u),mult(v,u)),op_t(v,u)),
file('GRP731-1.p',unknown),
[] ).
cnf(21,axiom,
equal(asoc(asoc(u,v,w),x,y),unit),
file('GRP731-1.p',unknown),
[] ).
cnf(22,axiom,
equal(asoc(u,v,asoc(w,x,y)),unit),
file('GRP731-1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(op_k(asoc(a,b,c),d),unit),
file('GRP731-1.p',unknown),
[] ).
cnf(42,plain,
equal(rd(unit,u),i(u)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(44,plain,
equal(rd(unit,i(u)),u),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(46,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[42,44]),
[iquote('0:Rew:42.0,44.0')] ).
cnf(50,plain,
equal(rd(u,mult(v,u)),i(v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(65,plain,
equal(mult(u,mult(i(u),v)),v),
inference(spr,[status(thm),theory(equality)],[46,6]),
[iquote('0:SpR:46.0,6.0')] ).
cnf(80,plain,
equal(i(rd(u,v)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[8,50]),
[iquote('0:SpR:8.0,50.0')] ).
cnf(161,plain,
equal(rd(i(u),i(mult(v,u))),i(i(v))),
inference(spr,[status(thm),theory(equality)],[5,50]),
[iquote('0:SpR:5.0,50.0')] ).
cnf(165,plain,
equal(mult(u,i(mult(u,v))),i(v)),
inference(spr,[status(thm),theory(equality)],[5,65]),
[iquote('0:SpR:5.0,65.0')] ).
cnf(168,plain,
equal(i(mult(u,i(v))),mult(i(u),v)),
inference(spr,[status(thm),theory(equality)],[46,5]),
[iquote('0:SpR:46.0,5.0')] ).
cnf(169,plain,
equal(mult(i(u),rd(v,w)),i(mult(u,rd(w,v)))),
inference(spr,[status(thm),theory(equality)],[80,5]),
[iquote('0:SpR:80.0,5.0')] ).
cnf(171,plain,
equal(i(mult(i(u),v)),mult(u,i(v))),
inference(spr,[status(thm),theory(equality)],[46,5]),
[iquote('0:SpR:46.0,5.0')] ).
cnf(172,plain,
equal(mult(rd(u,v),i(w)),i(mult(rd(v,u),w))),
inference(spr,[status(thm),theory(equality)],[80,5]),
[iquote('0:SpR:80.0,5.0')] ).
cnf(177,plain,
equal(rd(i(u),i(mult(v,u))),v),
inference(rew,[status(thm),theory(equality)],[46,161]),
[iquote('0:Rew:46.0,161.0')] ).
cnf(217,plain,
equal(rd(i(u),i(v)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[8,177]),
[iquote('0:SpR:8.0,177.0')] ).
cnf(250,plain,
equal(mult(u,op_t(v,u)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[14,65]),
[iquote('0:SpR:14.0,65.0')] ).
cnf(292,plain,
equal(mult(i(mult(u,v)),mult(v,u)),op_k(v,u)),
inference(spr,[status(thm),theory(equality)],[11,6]),
[iquote('0:SpR:11.0,6.0')] ).
cnf(806,plain,
equal(mult(u,mult(rd(v,u),mult(u,w))),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[8,9]),
[iquote('0:SpR:8.0,9.0')] ).
cnf(852,plain,
equal(mult(i(u),mult(i(v),w)),i(mult(u,mult(v,i(w))))),
inference(spr,[status(thm),theory(equality)],[168,5]),
[iquote('0:SpR:168.0,5.0')] ).
cnf(973,plain,
equal(mult(mult(u,v),i(mult(u,mult(v,w)))),i(op_l(w,v,u))),
inference(spr,[status(thm),theory(equality)],[12,171]),
[iquote('0:SpR:12.0,171.0')] ).
cnf(978,plain,
equal(mult(i(mult(u,i(v))),mult(u,unit)),op_l(v,i(v),u)),
inference(spr,[status(thm),theory(equality)],[4,12]),
[iquote('0:SpR:4.0,12.0')] ).
cnf(981,plain,
equal(mult(i(mult(u,v)),mult(u,unit)),op_l(i(v),v,u)),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(993,plain,
equal(mult(i(mult(i(mult(u,v)),u)),unit),op_l(v,u,i(mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[4,12]),
[iquote('0:SpR:4.0,12.0')] ).
cnf(1012,plain,
equal(mult(i(i(mult(u,v))),mult(i(u),mult(i(v),w))),op_l(w,i(v),i(u))),
inference(spr,[status(thm),theory(equality)],[5,12]),
[iquote('0:SpR:5.0,12.0')] ).
cnf(1025,plain,
equal(mult(i(mult(u,v)),u),op_l(i(v),v,u)),
inference(rew,[status(thm),theory(equality)],[2,981]),
[iquote('0:Rew:2.0,981.0')] ).
cnf(1026,plain,
equal(mult(mult(i(u),v),u),op_l(v,i(v),u)),
inference(rew,[status(thm),theory(equality)],[168,978,2]),
[iquote('0:Rew:168.0,978.0,2.0,978.0')] ).
cnf(1037,plain,
equal(op_l(u,v,i(mult(v,u))),mult(mult(v,u),i(v))),
inference(rew,[status(thm),theory(equality)],[2,993,171]),
[iquote('0:Rew:2.0,993.0,171.0,993.0')] ).
cnf(1042,plain,
equal(mult(mult(u,v),mult(i(u),mult(i(v),w))),op_l(w,i(v),i(u))),
inference(rew,[status(thm),theory(equality)],[46,1012]),
[iquote('0:Rew:46.0,1012.0')] ).
cnf(1043,plain,
equal(op_l(u,i(v),i(w)),i(op_l(i(u),v,w))),
inference(rew,[status(thm),theory(equality)],[973,1042,852]),
[iquote('0:Rew:973.0,1042.0,852.0,1042.0')] ).
cnf(1809,plain,
equal(mult(mult(u,mult(v,asoc(w,x,y))),unit),mult(mult(u,v),asoc(w,x,y))),
inference(spr,[status(thm),theory(equality)],[22,10]),
[iquote('0:SpR:22.0,10.0')] ).
cnf(1811,plain,
equal(mult(mult(asoc(u,v,w),mult(x,y)),unit),mult(mult(asoc(u,v,w),x),y)),
inference(spr,[status(thm),theory(equality)],[21,10]),
[iquote('0:SpR:21.0,10.0')] ).
cnf(1852,plain,
equal(mult(mult(u,v),asoc(w,x,y)),mult(u,mult(v,asoc(w,x,y)))),
inference(rew,[status(thm),theory(equality)],[2,1809]),
[iquote('0:Rew:2.0,1809.0')] ).
cnf(1853,plain,
equal(mult(u,mult(mult(v,w),asoc(u,v,w))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[1852,10]),
[iquote('0:Rew:1852.0,10.0')] ).
cnf(1856,plain,
equal(mult(u,mult(v,mult(w,asoc(u,v,w)))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[1852,1853]),
[iquote('0:Rew:1852.0,1853.0')] ).
cnf(1857,plain,
equal(mult(mult(asoc(u,v,w),x),y),mult(asoc(u,v,w),mult(x,y))),
inference(rew,[status(thm),theory(equality)],[2,1811]),
[iquote('0:Rew:2.0,1811.0')] ).
cnf(2031,plain,
equal(mult(i(u),mult(mult(u,v),w)),mult(v,mult(w,asoc(u,v,w)))),
inference(spr,[status(thm),theory(equality)],[1856,6]),
[iquote('0:SpR:1856.0,6.0')] ).
cnf(2039,plain,
equal(mult(i(mult(u,v)),mult(mult(u,v),w)),op_l(mult(w,asoc(u,v,w)),v,u)),
inference(spr,[status(thm),theory(equality)],[1856,12]),
[iquote('0:SpR:1856.0,12.0')] ).
cnf(2078,plain,
equal(op_l(mult(u,asoc(v,w,u)),w,v),u),
inference(rew,[status(thm),theory(equality)],[6,2039]),
[iquote('0:Rew:6.0,2039.0')] ).
cnf(3867,plain,
equal(op_l(mult(u,unit),v,asoc(w,x,y)),u),
inference(spr,[status(thm),theory(equality)],[21,2078]),
[iquote('0:SpR:21.0,2078.0')] ).
cnf(3884,plain,
equal(op_l(u,v,asoc(w,x,y)),u),
inference(rew,[status(thm),theory(equality)],[2,3867]),
[iquote('0:Rew:2.0,3867.0')] ).
cnf(5523,plain,
equal(mult(mult(i(asoc(u,v,w)),x),asoc(u,v,w)),x),
inference(spr,[status(thm),theory(equality)],[1026,3884]),
[iquote('0:SpR:1026.0,3884.0')] ).
cnf(5563,plain,
equal(mult(i(asoc(u,v,w)),mult(x,asoc(u,v,w))),x),
inference(rew,[status(thm),theory(equality)],[1852,5523]),
[iquote('0:Rew:1852.0,5523.0')] ).
cnf(5564,plain,
equal(op_t(u,asoc(v,w,x)),u),
inference(rew,[status(thm),theory(equality)],[14,5563]),
[iquote('0:Rew:14.0,5563.0')] ).
cnf(6155,plain,
equal(i(op_l(i(mult(u,asoc(i(v),i(w),u))),w,v)),u),
inference(spr,[status(thm),theory(equality)],[1043,2078]),
[iquote('0:SpR:1043.0,2078.0')] ).
cnf(8740,plain,
equal(op_l(i(u),i(v),i(i(mult(v,u)))),mult(i(mult(v,u)),i(i(v)))),
inference(spr,[status(thm),theory(equality)],[5,1037]),
[iquote('0:SpR:5.0,1037.0')] ).
cnf(8784,plain,
equal(op_l(i(u),i(v),mult(v,u)),mult(i(mult(v,u)),v)),
inference(rew,[status(thm),theory(equality)],[46,8740]),
[iquote('0:Rew:46.0,8740.0,46.0,8740.0')] ).
cnf(12990,plain,
equal(mult(i(u),mult(mult(u,v),w)),mult(rd(v,u),mult(u,w))),
inference(spr,[status(thm),theory(equality)],[806,6]),
[iquote('0:SpR:806.0,6.0')] ).
cnf(13045,plain,
equal(mult(u,mult(rd(v,u),unit)),mult(mult(u,v),i(u))),
inference(spr,[status(thm),theory(equality)],[3,806]),
[iquote('0:SpR:3.0,806.0')] ).
cnf(13046,plain,
equal(mult(mult(u,v),i(mult(u,w))),mult(u,mult(rd(v,u),i(w)))),
inference(spr,[status(thm),theory(equality)],[165,806]),
[iquote('0:SpR:165.0,806.0')] ).
cnf(13111,plain,
equal(mult(mult(u,v),i(u)),mult(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[2,13045]),
[iquote('0:Rew:2.0,13045.0')] ).
cnf(13112,plain,
equal(op_l(u,v,i(mult(v,u))),mult(v,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[13111,1037]),
[iquote('0:Rew:13111.0,1037.0')] ).
cnf(13168,plain,
equal(mult(rd(u,v),mult(v,w)),mult(u,mult(w,asoc(v,u,w)))),
inference(rew,[status(thm),theory(equality)],[12990,2031]),
[iquote('0:Rew:12990.0,2031.0')] ).
cnf(13184,plain,
equal(mult(mult(u,v),i(mult(u,w))),mult(u,i(mult(rd(u,v),w)))),
inference(rew,[status(thm),theory(equality)],[172,13046]),
[iquote('0:Rew:172.0,13046.0')] ).
cnf(13193,plain,
equal(mult(u,i(mult(rd(u,v),mult(v,w)))),i(op_l(w,v,u))),
inference(rew,[status(thm),theory(equality)],[13184,973]),
[iquote('0:Rew:13184.0,973.0')] ).
cnf(13611,plain,
equal(op_l(i(u),i(v),i(i(mult(v,u)))),mult(i(v),rd(i(u),i(v)))),
inference(spr,[status(thm),theory(equality)],[5,13112]),
[iquote('0:SpR:5.0,13112.0')] ).
cnf(13666,plain,
equal(op_l(i(u),i(v),mult(v,u)),mult(i(v),rd(v,u))),
inference(rew,[status(thm),theory(equality)],[46,13611,217]),
[iquote('0:Rew:46.0,13611.0,217.0,13611.0')] ).
cnf(13667,plain,
equal(mult(i(mult(u,v)),u),i(mult(u,rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[8784,13666,169]),
[iquote('0:Rew:8784.0,13666.0,169.0,13666.0')] ).
cnf(13668,plain,
equal(i(mult(u,rd(v,u))),op_l(i(v),v,u)),
inference(rew,[status(thm),theory(equality)],[13667,1025]),
[iquote('0:Rew:13667.0,1025.0')] ).
cnf(14479,plain,
equal(mult(u,op_l(i(v),v,u)),i(rd(v,u))),
inference(spr,[status(thm),theory(equality)],[13668,165]),
[iquote('0:SpR:13668.0,165.0')] ).
cnf(14534,plain,
equal(mult(u,op_l(i(v),v,u)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[80,14479]),
[iquote('0:Rew:80.0,14479.0')] ).
cnf(23915,plain,
equal(mult(u,i(mult(rd(u,v),mult(v,w)))),i(mult(w,asoc(v,u,w)))),
inference(spr,[status(thm),theory(equality)],[13168,165]),
[iquote('0:SpR:13168.0,165.0')] ).
cnf(24059,plain,
equal(i(mult(u,asoc(v,w,u))),i(op_l(u,v,w))),
inference(rew,[status(thm),theory(equality)],[13193,23915]),
[iquote('0:Rew:13193.0,23915.0')] ).
cnf(24066,plain,
equal(i(op_l(i(op_l(u,i(v),i(w))),w,v)),u),
inference(rew,[status(thm),theory(equality)],[24059,6155]),
[iquote('0:Rew:24059.0,6155.0')] ).
cnf(24067,plain,
equal(i(op_l(op_l(i(u),v,w),w,v)),u),
inference(rew,[status(thm),theory(equality)],[46,24066,1043]),
[iquote('0:Rew:46.0,24066.0,1043.0,24066.0')] ).
cnf(24355,plain,
equal(i(op_l(i(op_l(i(i(u)),v,w)),i(w),i(v))),u),
inference(spr,[status(thm),theory(equality)],[1043,24067]),
[iquote('0:SpR:1043.0,24067.0')] ).
cnf(24447,plain,
equal(op_l(op_l(u,v,w),w,v),u),
inference(rew,[status(thm),theory(equality)],[46,24355,1043]),
[iquote('0:Rew:46.0,24355.0,46.0,24355.0,1043.0,24355.0,46.0,24355.0')] ).
cnf(24728,plain,
equal(mult(u,asoc(v,w,u)),op_l(u,v,w)),
inference(spr,[status(thm),theory(equality)],[2078,24447]),
[iquote('0:SpR:2078.0,24447.0')] ).
cnf(24759,plain,
equal(mult(u,mult(v,op_l(w,u,v))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[24728,1856]),
[iquote('0:Rew:24728.0,1856.0')] ).
cnf(25430,plain,
equal(mult(mult(u,asoc(v,w,x)),y),mult(u,mult(asoc(v,w,x),y))),
inference(spr,[status(thm),theory(equality)],[3884,24759]),
[iquote('0:SpR:3884.0,24759.0')] ).
cnf(30823,plain,
equal(rd(asoc(u,v,w),mult(x,mult(y,asoc(u,v,w)))),i(mult(x,y))),
inference(spr,[status(thm),theory(equality)],[1852,50]),
[iquote('0:SpR:1852.0,50.0')] ).
cnf(30840,plain,
equal(mult(i(mult(u,mult(v,asoc(w,x,y)))),mult(asoc(w,x,y),mult(u,v))),op_k(asoc(w,x,y),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1852,292]),
[iquote('0:SpR:1852.0,292.0')] ).
cnf(31725,plain,
equal(mult(asoc(u,v,w),mult(op_t(x,asoc(u,v,w)),y)),mult(mult(x,asoc(u,v,w)),y)),
inference(spr,[status(thm),theory(equality)],[250,1857]),
[iquote('0:SpR:250.0,1857.0')] ).
cnf(31730,plain,
equal(mult(asoc(u,v,w),mult(op_l(i(x),x,asoc(u,v,w)),y)),mult(rd(asoc(u,v,w),x),y)),
inference(spr,[status(thm),theory(equality)],[14534,1857]),
[iquote('0:SpR:14534.0,1857.0')] ).
cnf(31774,plain,
equal(mult(mult(u,asoc(v,w,x)),y),mult(asoc(v,w,x),mult(u,y))),
inference(rew,[status(thm),theory(equality)],[5564,31725]),
[iquote('0:Rew:5564.0,31725.0')] ).
cnf(31775,plain,
equal(mult(u,mult(asoc(v,w,x),y)),mult(asoc(v,w,x),mult(u,y))),
inference(rew,[status(thm),theory(equality)],[25430,31774]),
[iquote('0:Rew:25430.0,31774.0')] ).
cnf(31778,plain,
equal(mult(asoc(u,v,w),mult(i(mult(x,mult(y,asoc(u,v,w)))),mult(x,y))),op_k(asoc(u,v,w),mult(x,y))),
inference(rew,[status(thm),theory(equality)],[31775,30840]),
[iquote('0:Rew:31775.0,30840.0')] ).
cnf(31805,plain,
equal(mult(asoc(u,v,w),mult(i(x),y)),mult(rd(asoc(u,v,w),x),y)),
inference(rew,[status(thm),theory(equality)],[3884,31730]),
[iquote('0:Rew:3884.0,31730.0')] ).
cnf(31831,plain,
equal(mult(i(mult(u,v)),mult(u,v)),op_k(asoc(w,x,y),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[30823,31778,31805]),
[iquote('0:Rew:30823.0,31778.0,31805.0,31778.0')] ).
cnf(31832,plain,
equal(op_k(asoc(u,v,w),mult(x,y)),unit),
inference(rew,[status(thm),theory(equality)],[4,31831]),
[iquote('0:Rew:4.0,31831.0')] ).
cnf(31926,plain,
equal(op_k(asoc(u,v,w),x),unit),
inference(spr,[status(thm),theory(equality)],[1,31832]),
[iquote('0:SpR:1.0,31832.0')] ).
cnf(32002,plain,
$false,
inference(unc,[status(thm)],[31926,23]),
[iquote('0:UnC:31926.0,23.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP731-1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 11:59:05 EDT 2022
% 0.15/0.36 % CPUTime :
% 23.64/23.82
% 23.64/23.82 SPASS V 3.9
% 23.64/23.82 SPASS beiseite: Proof found.
% 23.64/23.82 % SZS status Theorem
% 23.64/23.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.64/23.82 SPASS derived 19993 clauses, backtracked 0 clauses, performed 0 splits and kept 6126 clauses.
% 23.64/23.82 SPASS allocated 105646 KBytes.
% 23.64/23.82 SPASS spent 0:0:23.42 on the problem.
% 23.64/23.82 0:00:00.04 for the input.
% 23.64/23.82 0:00:00.00 for the FLOTTER CNF translation.
% 23.64/23.82 0:00:00.16 for inferences.
% 23.64/23.82 0:00:00.00 for the backtracking.
% 23.64/23.82 0:0:23.17 for the reduction.
% 23.64/23.82
% 23.64/23.82
% 23.64/23.82 Here is a proof with depth 5, length 96 :
% 23.64/23.82 % SZS output start Refutation
% See solution above
% 23.94/24.18 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 c09 c10 c11 c12 c14 c21 c22 goals
% 23.94/24.18
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