%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.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 01:07:20 PM UTC 2026
% Result : Unsatisfiable 0.65s 0.94s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 19 unt; 0 nHn; 27 RR)
% Number of literals : 37 ( 0 equ; 11 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 : 9 ( 9 usr; 7 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('LCL364-1.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('LCL364-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL364-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL364-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(x__dfg),y__dfg),implies__dfg(z__dfg,implies__dfg(implies__dfg(y__dfg,x__dfg),x__dfg)))),
file('LCL364-1.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(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(18,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(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(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)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
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(30,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[21,3]),
[iquote('0:SoR:21.0,3.0')] ).
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)],[17,1]),
[iquote('0:Res:17.0,1.1')] ).
cnf(110,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(114,plain,
is_a_theorem(implies__dfg(implies__dfg(u,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,18]),
[iquote('0:SoR:35.0,18.0')] ).
cnf(124,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[21,114]),
[iquote('0:SoR:21.0,114.0')] ).
cnf(127,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)],[13,124]),
[iquote('0:SoR:13.0,124.0')] ).
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)],[127,1]),
[iquote('0:Res:127.0,1.1')] ).
cnf(224,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[168,110]),
[iquote('0:SoR:168.0,110.0')] ).
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)],[224,1]),
[iquote('0:Res:224.0,1.1')] ).
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(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(implies__dfg(not__dfg(u),u),v))) ),
inference(sor,[status(thm)],[268,19]),
[iquote('0:SoR:268.1,19.0')] ).
cnf(1073,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(v),v),v))),
inference(sor,[status(thm)],[314,30]),
[iquote('0:SoR:314.0,30.0')] ).
cnf(1094,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)],[13,1073]),
[iquote('0:SoR:13.0,1073.0')] ).
cnf(1255,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)],[35,1094]),
[iquote('0:SoR:35.0,1094.0')] ).
cnf(1297,plain,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(w,implies__dfg(implies__dfg(v,u),u)))),
inference(sor,[status(thm)],[35,1255]),
[iquote('0:SoR:35.0,1255.0')] ).
cnf(1303,plain,
$false,
inference(unc,[status(thm)],[1297,5]),
[iquote('0:UnC:1297.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL364-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 20:35:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.65/0.94
% 0.65/0.94 SPASS V 3.9
% 0.65/0.94 SPASS beiseite: Proof found.
% 0.65/0.94 % SZS status Theorem
% 0.65/0.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.65/0.94 SPASS derived 1263 clauses, backtracked 0 clauses, performed 0 splits and kept 663 clauses.
% 0.65/0.94 SPASS allocated 78067 KBytes.
% 0.65/0.94 SPASS spent 0:00:00.55 on the problem.
% 0.65/0.94 0:00:00.06 for the input.
% 0.65/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.65/0.94 0:00:00.06 for inferences.
% 0.65/0.94 0:00:00.00 for the backtracking.
% 0.65/0.94 0:00:00.38 for the reduction.
% 0.65/0.94
% 0.65/0.94
% 0.65/0.94 Here is a proof with depth 15, length 27 :
% 0.65/0.94 % SZS output start Refutation
% See solution above
% 0.65/0.94 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_13
% 0.65/0.94
%------------------------------------------------------------------------------