%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL362-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 01:07:19 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.54s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 16 unt; 0 nHn; 24 RR)
% Number of literals : 34 ( 0 equ; 12 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 : 8 ( 8 usr; 6 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('LCL362-1.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('LCL362-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL362-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL362-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(x__dfg,implies__dfg(implies__dfg(not__dfg(y__dfg),y__dfg),y__dfg)),implies__dfg(implies__dfg(not__dfg(y__dfg),y__dfg),y__dfg))),
file('LCL362-1.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,not__dfg(v)),implies__dfg(v,implies__dfg(u,w)))),
inference(sor,[status(thm)],[35,18]),
[iquote('0:SoR:35.0,18.0')] ).
cnf(111,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(124,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(not__dfg(u),w)))),
inference(sor,[status(thm)],[21,110]),
[iquote('0:SoR:21.0,110.0')] ).
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(231,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
inference(sor,[status(thm)],[168,111]),
[iquote('0:SoR:168.0,111.0')] ).
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)],[231,1]),
[iquote('0:Res:231.0,1.1')] ).
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(318,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(sor,[status(thm)],[268,30]),
[iquote('0:SoR:268.1,30.0')] ).
cnf(346,plain,
~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(y__dfg),y__dfg),y__dfg)),
inference(res,[status(thm),theory(equality)],[318,5]),
[iquote('0:Res:318.1,5.0')] ).
cnf(347,plain,
$false,
inference(ssi,[status(thm)],[346,3]),
[iquote('0:SSi:346.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL362-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 21:53:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.22/0.54
% 0.22/0.54 SPASS V 3.9
% 0.22/0.54 SPASS beiseite: Proof found.
% 0.22/0.54 % SZS status Theorem
% 0.22/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.54 SPASS derived 330 clauses, backtracked 0 clauses, performed 0 splits and kept 209 clauses.
% 0.22/0.54 SPASS allocated 76265 KBytes.
% 0.22/0.54 SPASS spent 0:00:00.16 on the problem.
% 0.22/0.54 0:00:00.06 for the input.
% 0.22/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.54 0:00:00.01 for inferences.
% 0.22/0.54 0:00:00.00 for the backtracking.
% 0.22/0.54 0:00:00.04 for the reduction.
% 0.22/0.54
% 0.22/0.54
% 0.22/0.54 Here is a proof with depth 12, length 24 :
% 0.22/0.54 % SZS output start Refutation
% See solution above
% 0.22/0.54 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_11
% 0.22/0.54
%------------------------------------------------------------------------------