%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 01:07:11 PM UTC 2026
% Result : Unsatisfiable 8.06s 8.32s
% Output : Refutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 67 ( 44 unt; 0 nHn; 67 RR)
% Number of literals : 93 ( 0 equ; 27 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 : 7 ( 7 usr; 5 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('LCL256-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL256-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL256-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL256-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(not__dfg(not__dfg(implies__dfg(p,p)))),
file('LCL256-1.p',unknown),
[] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(17,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[13,2]),
[iquote('0:SoR:13.0,2.0')] ).
cnf(19,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(not__dfg(u),u),v))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w))),
inference(sor,[status(thm)],[13,17]),
[iquote('0:SoR:13.0,17.0')] ).
cnf(21,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(u,w)) ),
inference(res,[status(thm),theory(equality)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(22,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w),implies__dfg(implies__dfg(u,v),w))),
inference(sor,[status(thm)],[13,19]),
[iquote('0:SoR:13.0,19.0')] ).
cnf(23,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),v)) ),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(35,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(56,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),implies__dfg(not__dfg(u),v))),
inference(sor,[status(thm)],[23,4]),
[iquote('0:SoR:23.0,4.0')] ).
cnf(61,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(u),u)),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[23,3]),
[iquote('0:SoR:23.0,3.0')] ).
cnf(79,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),x),v),w)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(91,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),v),w))
| is_a_theorem(implies__dfg(implies__dfg(u,v),w)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.0,1.1')] ).
cnf(116,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,17]),
[iquote('0:SoR:35.0,17.0')] ).
cnf(117,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,22]),
[iquote('0:SoR:35.0,22.0')] ).
cnf(122,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[21,116]),
[iquote('0:SoR:21.0,116.0')] ).
cnf(125,plain,
( ~ is_a_theorem(implies__dfg(u,not__dfg(v)))
| is_a_theorem(implies__dfg(v,implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[116,1]),
[iquote('0:Res:116.0,1.1')] ).
cnf(129,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x),implies__dfg(v,x))),
inference(sor,[status(thm)],[13,122]),
[iquote('0:SoR:13.0,122.0')] ).
cnf(168,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),w)),x))
| is_a_theorem(implies__dfg(v,x)) ),
inference(res,[status(thm),theory(equality)],[129,1]),
[iquote('0:Res:129.0,1.1')] ).
cnf(202,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[117,1]),
[iquote('0:Res:117.0,1.1')] ).
cnf(236,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[168,117]),
[iquote('0:SoR:168.0,117.0')] ).
cnf(246,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[236,1]),
[iquote('0:Res:236.0,1.1')] ).
cnf(268,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[246,1]),
[iquote('0:Res:246.1,1.1')] ).
cnf(314,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(x,implies__dfg(u,w))) ),
inference(sor,[status(thm)],[268,17]),
[iquote('0:SoR:268.1,17.0')] ).
cnf(377,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[79,56]),
[iquote('0:SoR:79.0,56.0')] ).
cnf(391,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),v),implies__dfg(not__dfg(u),u)),u)),
inference(sor,[status(thm)],[79,61]),
[iquote('0:SoR:79.0,61.0')] ).
cnf(393,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u),u)),
inference(sor,[status(thm)],[79,3]),
[iquote('0:SoR:79.0,3.0')] ).
cnf(396,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u),u)),
inference(sor,[status(thm)],[79,393]),
[iquote('0:SoR:79.0,393.0')] ).
cnf(480,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),v),u))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(res,[status(thm),theory(equality)],[377,1]),
[iquote('0:Res:377.0,1.1')] ).
cnf(498,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),v)),w),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[396,1]),
[iquote('0:Res:396.0,1.1')] ).
cnf(1284,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[314,61]),
[iquote('0:SoR:314.0,61.0')] ).
cnf(1286,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(sor,[status(thm)],[314,3]),
[iquote('0:SoR:314.0,3.0')] ).
cnf(1301,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1286]),
[iquote('0:SoR:13.0,1286.0')] ).
cnf(1357,plain,
is_a_theorem(implies__dfg(not__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u)),v)),
inference(sor,[status(thm)],[480,1284]),
[iquote('0:SoR:480.0,1284.0')] ).
cnf(1368,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[13,1284]),
[iquote('0:SoR:13.0,1284.0')] ).
cnf(1469,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[1301,1]),
[iquote('0:Res:1301.0,1.1')] ).
cnf(2112,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(w,implies__dfg(u,v)))),
inference(sor,[status(thm)],[35,1368]),
[iquote('0:SoR:35.0,1368.0')] ).
cnf(2133,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(not__dfg(implies__dfg(not__dfg(u),u)))),u)),
inference(sor,[status(thm)],[35,391]),
[iquote('0:SoR:35.0,391.0')] ).
cnf(2559,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,w),u),v))),
inference(sor,[status(thm)],[202,1301]),
[iquote('0:SoR:202.0,1301.0')] ).
cnf(2560,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(implies__dfg(u,v),w))) ),
inference(sor,[status(thm)],[202,246]),
[iquote('0:SoR:202.0,246.1')] ).
cnf(2597,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
inference(sor,[status(thm)],[1469,2559]),
[iquote('0:SoR:1469.0,2559.0')] ).
cnf(2606,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
inference(sor,[status(thm)],[498,2597]),
[iquote('0:SoR:498.0,2597.0')] ).
cnf(2643,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[2606,1]),
[iquote('0:Res:2606.0,1.1')] ).
cnf(3583,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
inference(sor,[status(thm)],[168,2112]),
[iquote('0:SoR:168.0,2112.0')] ).
cnf(3611,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[202,3583]),
[iquote('0:SoR:202.0,3583.0')] ).
cnf(3635,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(res,[status(thm),theory(equality)],[3611,1]),
[iquote('0:Res:3611.0,1.1')] ).
cnf(3974,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(u),u))),u)),
inference(sor,[status(thm)],[3635,2133]),
[iquote('0:SoR:3635.0,2133.0')] ).
cnf(4163,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)))),v))),
inference(sor,[status(thm)],[125,3974]),
[iquote('0:SoR:125.0,3974.0')] ).
cnf(5509,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[2643,2560]),
[iquote('0:SoR:2643.0,2560.1')] ).
cnf(5755,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),u))
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[91,5509]),
[iquote('0:SoR:91.0,5509.1')] ).
cnf(5776,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[5509,1]),
[iquote('0:Res:5509.1,1.1')] ).
cnf(6187,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),u),u),v),v)),
inference(sor,[status(thm)],[5755,1357]),
[iquote('0:SoR:5755.0,1357.0')] ).
cnf(6403,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(not__dfg(v),v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[35,6187]),
[iquote('0:SoR:35.0,6187.0')] ).
cnf(7070,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(v),v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[5776,6403]),
[iquote('0:SoR:5776.1,6403.0')] ).
cnf(8430,plain,
is_a_theorem(implies__dfg(u,not__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u))))),
inference(sor,[status(thm)],[7070,4163]),
[iquote('0:SoR:7070.0,4163.0')] ).
cnf(8552,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(not__dfg(u)),not__dfg(u)),implies__dfg(u,v))),
inference(sor,[status(thm)],[125,8430]),
[iquote('0:SoR:125.0,8430.0')] ).
cnf(8700,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[21,8552]),
[iquote('0:SoR:21.0,8552.0')] ).
cnf(8718,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(sor,[status(thm)],[7070,8700]),
[iquote('0:SoR:7070.0,8700.0')] ).
cnf(8746,plain,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(not__dfg(not__dfg(u))),v))),
inference(sor,[status(thm)],[125,8718]),
[iquote('0:SoR:125.0,8718.0')] ).
cnf(8799,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[7070,8746]),
[iquote('0:SoR:7070.0,8746.0')] ).
cnf(8824,plain,
is_a_theorem(not__dfg(not__dfg(implies__dfg(u,u)))),
inference(sor,[status(thm)],[2643,8799]),
[iquote('0:SoR:2643.0,8799.0')] ).
cnf(8845,plain,
$false,
inference(unc,[status(thm)],[8824,5]),
[iquote('0:UnC:8824.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL256-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 23:26:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 8.06/8.32
% 8.06/8.32 SPASS V 3.9
% 8.06/8.32 SPASS beiseite: Proof found.
% 8.06/8.32 % SZS status Theorem
% 8.06/8.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.06/8.32 SPASS derived 8777 clauses, backtracked 0 clauses, performed 0 splits and kept 3344 clauses.
% 8.06/8.32 SPASS allocated 87161 KBytes.
% 8.06/8.32 SPASS spent 0:00:07.94 on the problem.
% 8.06/8.32 0:00:00.09 for the input.
% 8.06/8.32 0:00:00.00 for the FLOTTER CNF translation.
% 8.06/8.32 0:00:00.53 for inferences.
% 8.06/8.32 0:00:00.00 for the backtracking.
% 8.06/8.32 0:00:07.22 for the reduction.
% 8.06/8.32
% 8.06/8.32
% 8.06/8.32 Here is a proof with depth 29, length 67 :
% 8.06/8.32 % SZS output start Refutation
% See solution above
% 8.26/8.56 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_not_not_implies
% 8.26/8.56
%------------------------------------------------------------------------------