TSTP Solution File: LCL095-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL095-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 14:34:34 EDT 2022
% Result : Unsatisfiable 1.34s 1.51s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of clauses : 67 ( 43 unt; 0 nHn; 67 RR)
% Number of literals : 92 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL095-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)),implies__dfg(implies__dfg(x,u),implies__dfg(y,implies__dfg(w,u))))),
file('LCL095-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(implies__dfg(a,b),b))),
file('LCL095-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(implies__dfg(x,u),implies__dfg(y,implies__dfg(w,u)))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(w,x)),implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(w,x))))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,w)),implies__dfg(x,implies__dfg(y,v))),implies__dfg(z,implies__dfg(x1,implies__dfg(x,implies__dfg(y,v)))))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(w,x)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(implies__dfg(x,y),implies__dfg(y,w)))))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(implies__dfg(x,y),implies__dfg(y,w))))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(x,v))))),
inference(ems,[status(thm)],[14,8]),
[iquote('0:EmS:14.0,8.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,w)),x),implies__dfg(y,implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(y,x),implies__dfg(x,z))),implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(y,x),implies__dfg(x,z)))))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(x,implies__dfg(y,w)))))),
inference(sor,[status(thm)],[10,18]),
[iquote('0:SoR:10.0,18.0')] ).
cnf(35,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(x,implies__dfg(y,w))))) ),
inference(res,[status(thm),theory(equality)],[29,1]),
[iquote('0:Res:29.0,1.1')] ).
cnf(36,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(w,implies__dfg(x,v))))),
inference(ems,[status(thm)],[35,9]),
[iquote('0:EmS:35.0,9.0')] ).
cnf(43,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(y,implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,36]),
[iquote('0:SoR:7.0,36.0')] ).
cnf(54,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x))
| is_a_theorem(implies__dfg(y,implies__dfg(w,x))) ),
inference(res,[status(thm),theory(equality)],[43,1]),
[iquote('0:Res:43.0,1.1')] ).
cnf(60,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,implies__dfg(y,w)))))),
inference(sor,[status(thm)],[54,2]),
[iquote('0:SoR:54.0,2.0')] ).
cnf(61,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,x))),implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))),implies__dfg(x2,implies__dfg(x3,implies__dfg(y,implies__dfg(z,implies__dfg(x1,w))))))),
inference(sor,[status(thm)],[7,20]),
[iquote('0:SoR:7.0,20.0')] ).
cnf(65,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(y,x),implies__dfg(x,z))))
| is_a_theorem(implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(y,x),implies__dfg(x,z))))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(100,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),x),implies__dfg(x,implies__dfg(y,x)))))),
inference(sor,[status(thm)],[65,2]),
[iquote('0:SoR:65.0,2.0')] ).
cnf(119,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,y)))),implies__dfg(z,implies__dfg(implies__dfg(x1,y),implies__dfg(y,x2)))),implies__dfg(x3,implies__dfg(x4,implies__dfg(z,implies__dfg(implies__dfg(x1,y),implies__dfg(y,x2))))))),
inference(sor,[status(thm)],[7,61]),
[iquote('0:SoR:7.0,61.0')] ).
cnf(124,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,x))),implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))))
| is_a_theorem(implies__dfg(x2,implies__dfg(x3,implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))))) ),
inference(res,[status(thm),theory(equality)],[61,1]),
[iquote('0:Res:61.0,1.1')] ).
cnf(158,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(x,v))),y),implies__dfg(z,implies__dfg(u,y)))),
inference(sor,[status(thm)],[7,60]),
[iquote('0:SoR:7.0,60.0')] ).
cnf(165,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),v),implies__dfg(v,implies__dfg(w,v))),x),implies__dfg(y,implies__dfg(z,x)))),
inference(sor,[status(thm)],[7,100]),
[iquote('0:SoR:7.0,100.0')] ).
cnf(172,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),x),implies__dfg(x,implies__dfg(y,x))))) ),
inference(res,[status(thm),theory(equality)],[100,1]),
[iquote('0:Res:100.0,1.1')] ).
cnf(228,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),implies__dfg(y,implies__dfg(implies__dfg(z,w),w)))))),
inference(sor,[status(thm)],[124,2]),
[iquote('0:SoR:124.0,2.0')] ).
cnf(297,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(x,y)))),implies__dfg(z,implies__dfg(x1,implies__dfg(x2,implies__dfg(x3,x))))),implies__dfg(x4,implies__dfg(x5,implies__dfg(z,implies__dfg(x1,implies__dfg(x2,implies__dfg(x3,x)))))))),
inference(sor,[status(thm)],[7,119]),
[iquote('0:SoR:7.0,119.0')] ).
cnf(361,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),w),implies__dfg(w,implies__dfg(x,w))))),
inference(ems,[status(thm)],[172,119]),
[iquote('0:EmS:172.0,119.0')] ).
cnf(396,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),w),implies__dfg(w,implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[361,1]),
[iquote('0:Res:361.0,1.1')] ).
cnf(398,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),v),implies__dfg(v,implies__dfg(w,v)))),
inference(ems,[status(thm)],[396,119]),
[iquote('0:EmS:396.0,119.0')] ).
cnf(424,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(x,implies__dfg(v,implies__dfg(w,v))))),
inference(sor,[status(thm)],[7,398]),
[iquote('0:SoR:7.0,398.0')] ).
cnf(498,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,implies__dfg(implies__dfg(x,u),u))),y),implies__dfg(z,implies__dfg(x1,y)))),
inference(sor,[status(thm)],[7,228]),
[iquote('0:SoR:7.0,228.0')] ).
cnf(509,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),implies__dfg(y,implies__dfg(implies__dfg(z,w),w))))) ),
inference(res,[status(thm),theory(equality)],[228,1]),
[iquote('0:Res:228.0,1.1')] ).
cnf(550,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))
| is_a_theorem(implies__dfg(x,implies__dfg(v,implies__dfg(w,v)))) ),
inference(res,[status(thm),theory(equality)],[424,1]),
[iquote('0:Res:424.0,1.1')] ).
cnf(779,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,implies__dfg(y,z))))),implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(x3,z),implies__dfg(z,x4))))),implies__dfg(x5,implies__dfg(x6,implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(x3,z),implies__dfg(z,x4)))))))),
inference(sor,[status(thm)],[7,297]),
[iquote('0:SoR:7.0,297.0')] ).
cnf(896,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,implies__dfg(implies__dfg(y,v),v))))),
inference(ems,[status(thm)],[509,165]),
[iquote('0:EmS:509.0,165.0')] ).
cnf(957,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,implies__dfg(implies__dfg(y,v),v)))) ),
inference(res,[status(thm),theory(equality)],[896,1]),
[iquote('0:Res:896.0,1.1')] ).
cnf(1066,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,implies__dfg(implies__dfg(x,u),u)))),
inference(ems,[status(thm)],[957,165]),
[iquote('0:EmS:957.0,165.0')] ).
cnf(1122,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,implies__dfg(implies__dfg(x,u),u))) ),
inference(res,[status(thm),theory(equality)],[1066,1]),
[iquote('0:Res:1066.0,1.1')] ).
cnf(1158,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,implies__dfg(x,x))),implies__dfg(w,implies__dfg(x,x))))),
inference(sor,[status(thm)],[1122,43]),
[iquote('0:SoR:1122.0,43.0')] ).
cnf(1178,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(w,implies__dfg(x,x))),implies__dfg(w,implies__dfg(x,x)))) ),
inference(res,[status(thm),theory(equality)],[1158,1]),
[iquote('0:Res:1158.0,1.1')] ).
cnf(1201,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,w))),implies__dfg(v,implies__dfg(w,w)))),
inference(ems,[status(thm)],[1178,165]),
[iquote('0:EmS:1178.0,165.0')] ).
cnf(1251,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,implies__dfg(x,v)))),
inference(sor,[status(thm)],[7,1201]),
[iquote('0:SoR:7.0,1201.0')] ).
cnf(1266,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w))))
| is_a_theorem(implies__dfg(v,implies__dfg(w,w))) ),
inference(res,[status(thm),theory(equality)],[1201,1]),
[iquote('0:Res:1201.0,1.1')] ).
cnf(1596,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[1251,1]),
[iquote('0:Res:1251.0,1.1')] ).
cnf(1754,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,x))))),
inference(sor,[status(thm)],[1596,1201]),
[iquote('0:SoR:1596.0,1201.0')] ).
cnf(1826,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(x,x)))) ),
inference(res,[status(thm),theory(equality)],[1754,1]),
[iquote('0:Res:1754.0,1.1')] ).
cnf(1828,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
inference(ems,[status(thm)],[1826,498]),
[iquote('0:EmS:1826.0,498.0')] ).
cnf(1881,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(mrr,[status(thm)],[1266,1828]),
[iquote('0:MRR:1266.0,1828.0')] ).
cnf(1903,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[1881,1]),
[iquote('0:Res:1881.0,1.1')] ).
cnf(1918,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[1903,779]),
[iquote('0:EmS:1903.0,779.0')] ).
cnf(1983,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[550,1918]),
[iquote('0:SoR:550.0,1918.0')] ).
cnf(2049,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[1983,1]),
[iquote('0:Res:1983.0,1.1')] ).
cnf(2050,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[2049,1918]),
[iquote('0:EmS:2049.0,1918.0')] ).
cnf(2101,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,implies__dfg(x,u)))),
inference(sor,[status(thm)],[7,2050]),
[iquote('0:SoR:7.0,2050.0')] ).
cnf(2297,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,implies__dfg(x,u))) ),
inference(res,[status(thm),theory(equality)],[2101,1]),
[iquote('0:Res:2101.0,1.1')] ).
cnf(4447,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(w,implies__dfg(y,x)))))),
inference(sor,[status(thm)],[2297,158]),
[iquote('0:SoR:2297.0,158.0')] ).
cnf(4514,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(w,implies__dfg(y,x))))) ),
inference(res,[status(thm),theory(equality)],[4447,1]),
[iquote('0:Res:4447.0,1.1')] ).
cnf(4515,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,implies__dfg(x,w))))),
inference(ems,[status(thm)],[4514,1918]),
[iquote('0:EmS:4514.0,1918.0')] ).
cnf(4595,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(y,implies__dfg(implies__dfg(u,w),x)))),
inference(sor,[status(thm)],[7,4515]),
[iquote('0:SoR:7.0,4515.0')] ).
cnf(5890,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(implies__dfg(w,x),x))))),
inference(sor,[status(thm)],[2297,4595]),
[iquote('0:SoR:2297.0,4595.0')] ).
cnf(5930,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(implies__dfg(w,x),x)))) ),
inference(res,[status(thm),theory(equality)],[5890,1]),
[iquote('0:Res:5890.0,1.1')] ).
cnf(5931,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(v,w),w)))),
inference(ems,[status(thm)],[5930,1918]),
[iquote('0:EmS:5930.0,1918.0')] ).
cnf(6099,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(v,w),w))) ),
inference(res,[status(thm),theory(equality)],[5931,1]),
[iquote('0:Res:5931.0,1.1')] ).
cnf(6100,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
inference(ems,[status(thm)],[6099,1918]),
[iquote('0:EmS:6099.0,1918.0')] ).
cnf(6198,plain,
$false,
inference(unc,[status(thm)],[6100,3]),
[iquote('0:UnC:6100.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL095-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 12:37:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.34/1.51
% 1.34/1.51 SPASS V 3.9
% 1.34/1.51 SPASS beiseite: Proof found.
% 1.34/1.51 % SZS status Theorem
% 1.34/1.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.34/1.51 SPASS derived 6136 clauses, backtracked 0 clauses, performed 0 splits and kept 929 clauses.
% 1.34/1.51 SPASS allocated 82823 KBytes.
% 1.34/1.51 SPASS spent 0:00:01.16 on the problem.
% 1.34/1.51 0:00:00.04 for the input.
% 1.34/1.51 0:00:00.00 for the FLOTTER CNF translation.
% 1.34/1.51 0:00:00.15 for inferences.
% 1.34/1.51 0:00:00.00 for the backtracking.
% 1.34/1.51 0:00:00.93 for the reduction.
% 1.34/1.51
% 1.34/1.51
% 1.34/1.51 Here is a proof with depth 32, length 67 :
% 1.34/1.51 % SZS output start Refutation
% See solution above
% 1.36/1.55 Formulae used in the proof : condensed_detachment ic_JLukasiewicz_5 prove_ic_5
% 1.36/1.55
%------------------------------------------------------------------------------