%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:06:44 PM UTC 2026
% Result : Unsatisfiable 3.97s 4.23s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of clauses : 55 ( 28 unt; 0 nHn; 55 RR)
% Number of literals : 88 ( 0 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 11 ( 11 usr; 10 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('LCL083-2.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(w,u),implies__dfg(x,u)))),
file('LCL083-2.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(u,u)),
file('LCL083-2.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
file('LCL083-2.p',unknown),
[] ).
cnf(10,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(x,u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),implies__dfg(y,implies__dfg(v,x)))),
inference(sor,[status(thm)],[10,2]),
[iquote('0:SoR:10.0,2.0')] ).
cnf(12,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(sor,[status(thm)],[10,3]),
[iquote('0:SoR:10.0,3.0')] ).
cnf(13,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w)))),
inference(sor,[status(thm)],[10,12]),
[iquote('0:SoR:10.0,12.0')] ).
cnf(14,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,u)) ),
inference(res,[status(thm),theory(equality)],[12,1]),
[iquote('0:Res:12.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[14,12]),
[iquote('0:SoR:14.0,12.0')] ).
cnf(16,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[10,15]),
[iquote('0:SoR:10.0,15.0')] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(y,v))),implies__dfg(z,implies__dfg(implies__dfg(x,v),implies__dfg(y,v))))),
inference(sor,[status(thm)],[10,11]),
[iquote('0:SoR:10.0,11.0')] ).
cnf(24,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(v,x))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v)))),
inference(sor,[status(thm)],[21,2]),
[iquote('0:SoR:21.0,2.0')] ).
cnf(37,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u)),x),implies__dfg(y,x))),
inference(sor,[status(thm)],[10,29]),
[iquote('0:SoR:10.0,29.0')] ).
cnf(41,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,v)),implies__dfg(y,implies__dfg(x,v)))),
inference(sor,[status(thm)],[10,13]),
[iquote('0:SoR:10.0,13.0')] ).
cnf(70,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[24,16]),
[iquote('0:SoR:24.0,16.0')] ).
cnf(83,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[70,1]),
[iquote('0:Res:70.0,1.1')] ).
cnf(84,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[83,11]),
[iquote('0:EmS:83.0,11.0')] ).
cnf(98,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),v),implies__dfg(x,v))),
inference(sor,[status(thm)],[10,84]),
[iquote('0:SoR:10.0,84.0')] ).
cnf(101,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[84,1]),
[iquote('0:Res:84.0,1.1')] ).
cnf(103,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[10,101]),
[iquote('0:SoR:10.0,101.1')] ).
cnf(110,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(x,w))),implies__dfg(y,implies__dfg(w,z))),implies__dfg(x1,implies__dfg(y,implies__dfg(w,z))))),
inference(sor,[status(thm)],[10,22]),
[iquote('0:SoR:10.0,22.0')] ).
cnf(118,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
inference(sor,[status(thm)],[21,103]),
[iquote('0:SoR:21.0,103.1')] ).
cnf(121,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),implies__dfg(x,w))) ),
inference(sor,[status(thm)],[10,118]),
[iquote('0:SoR:10.0,118.1')] ).
cnf(189,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,implies__dfg(v,x))),implies__dfg(y,implies__dfg(w,implies__dfg(v,x))))),
inference(sor,[status(thm)],[10,98]),
[iquote('0:SoR:10.0,98.0')] ).
cnf(194,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,implies__dfg(w,y))),implies__dfg(z,implies__dfg(x,implies__dfg(w,y))))),
inference(sor,[status(thm)],[10,41]),
[iquote('0:SoR:10.0,41.0')] ).
cnf(198,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,v)))
| is_a_theorem(implies__dfg(y,implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[41,1]),
[iquote('0:Res:41.0,1.1')] ).
cnf(206,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(implies__dfg(v,u),w))
| is_a_theorem(implies__dfg(x,w)) ),
inference(res,[status(thm),theory(equality)],[121,1]),
[iquote('0:Res:121.1,1.1')] ).
cnf(248,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)))),implies__dfg(x2,implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)))))),
inference(sor,[status(thm)],[10,110]),
[iquote('0:SoR:10.0,110.0')] ).
cnf(438,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),x),w),implies__dfg(v,w)))),
inference(sor,[status(thm)],[198,2]),
[iquote('0:SoR:198.0,2.0')] ).
cnf(466,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),implies__dfg(x,w)))) ),
inference(sor,[status(thm)],[206,2]),
[iquote('0:SoR:206.1,2.0')] ).
cnf(484,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(y,x))) ),
inference(sor,[status(thm)],[10,466]),
[iquote('0:SoR:10.0,466.1')] ).
cnf(540,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,implies__dfg(w,y))))
| is_a_theorem(implies__dfg(z,implies__dfg(x,implies__dfg(w,y)))) ),
inference(res,[status(thm),theory(equality)],[194,1]),
[iquote('0:Res:194.0,1.1')] ).
cnf(677,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),x),w),implies__dfg(v,w))) ),
inference(res,[status(thm),theory(equality)],[438,1]),
[iquote('0:Res:438.0,1.1')] ).
cnf(1036,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x)))),
inference(sor,[status(thm)],[540,2]),
[iquote('0:SoR:540.0,2.0')] ).
cnf(1068,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x))) ),
inference(res,[status(thm),theory(equality)],[1036,1]),
[iquote('0:Res:1036.0,1.1')] ).
cnf(1077,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(ems,[status(thm)],[1068,248]),
[iquote('0:EmS:1068.0,248.0')] ).
cnf(1568,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),w),v),implies__dfg(u,v))),
inference(ems,[status(thm)],[677,1077]),
[iquote('0:EmS:677.0,1077.0')] ).
cnf(1622,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(u,v),w)),implies__dfg(x,implies__dfg(implies__dfg(u,v),w)))),
inference(sor,[status(thm)],[10,1568]),
[iquote('0:SoR:10.0,1568.0')] ).
cnf(3174,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u)),x))
| is_a_theorem(implies__dfg(y,x)) ),
inference(res,[status(thm),theory(equality)],[37,1]),
[iquote('0:Res:37.0,1.1')] ).
cnf(5859,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(y,x)) ),
inference(res,[status(thm),theory(equality)],[484,1]),
[iquote('0:Res:484.1,1.1')] ).
cnf(12011,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(implies__dfg(u,x),x)))) ),
inference(sor,[status(thm)],[5859,1622]),
[iquote('0:SoR:5859.1,1622.0')] ).
cnf(12012,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),w)))),
inference(sor,[status(thm)],[3174,1622]),
[iquote('0:SoR:3174.0,1622.0')] ).
cnf(12135,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),w))) ),
inference(res,[status(thm),theory(equality)],[12012,1]),
[iquote('0:Res:12012.0,1.1')] ).
cnf(12437,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(w,implies__dfg(implies__dfg(u,x),x))) ),
inference(res,[status(thm),theory(equality)],[12011,1]),
[iquote('0:Res:12011.1,1.1')] ).
cnf(12438,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),w))) ),
inference(con,[status(thm)],[12437]),
[iquote('0:Con:12437.1')] ).
cnf(12530,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(implies__dfg(implies__dfg(u,w),w)) ),
inference(res,[status(thm),theory(equality)],[12438,1]),
[iquote('0:Res:12438.1,1.1')] ).
cnf(12531,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(con,[status(thm)],[12530]),
[iquote('0:Con:12530.1')] ).
cnf(12609,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[12531,1]),
[iquote('0:Res:12531.1,1.1')] ).
cnf(12887,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),v))),
inference(ems,[status(thm)],[12135,189]),
[iquote('0:EmS:12135.0,189.0')] ).
cnf(13033,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),v)) ),
inference(sor,[status(thm)],[12609,12887]),
[iquote('0:SoR:12609.1,12887.0')] ).
cnf(13289,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
inference(ems,[status(thm)],[13033,189]),
[iquote('0:EmS:13033.0,189.0')] ).
cnf(13435,plain,
$false,
inference(unc,[status(thm)],[13289,4]),
[iquote('0:UnC:13289.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 13:57:12 UTC 2026
% 0.10/0.35 % CPUTime :
% 3.97/4.23
% 3.97/4.23 SPASS V 3.9
% 3.97/4.23 SPASS beiseite: Proof found.
% 3.97/4.23 % SZS status Theorem
% 3.97/4.23 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.97/4.23 SPASS derived 13207 clauses, backtracked 0 clauses, performed 0 splits and kept 1120 clauses.
% 3.97/4.23 SPASS allocated 84594 KBytes.
% 3.97/4.23 SPASS spent 0:00:03.62 on the problem.
% 3.97/4.23 0:00:00.06 for the input.
% 3.97/4.23 0:00:00.00 for the FLOTTER CNF translation.
% 3.97/4.23 0:00:00.53 for inferences.
% 3.97/4.23 0:00:00.00 for the backtracking.
% 3.97/4.23 0:00:02.96 for the reduction.
% 3.97/4.23
% 3.97/4.23
% 3.97/4.23 Here is a proof with depth 22, length 55 :
% 3.97/4.23 % SZS output start Refutation
% See solution above
% 3.97/4.23 Formulae used in the proof : condensed_detachment ic_JLukasiewicz ic_1 prove_ic_3
% 3.97/4.23
%------------------------------------------------------------------------------