%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL358-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 0.95s 1.24s
% Output : Refutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 0 equ; 6 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('LCL358-1.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('LCL358-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(x__dfg,implies__dfg(implies__dfg(y__dfg,z__dfg),u__dfg)),implies__dfg(implies__dfg(y__dfg,v__dfg),implies__dfg(x__dfg,implies__dfg(implies__dfg(v__dfg,z__dfg),u__dfg))))),
file('LCL358-1.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(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(113,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(x,v),implies__dfg(u,implies__dfg(x,w))))),
inference(sor,[status(thm)],[35,17]),
[iquote('0:SoR:35.0,17.0')] ).
cnf(115,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(u,w),x),implies__dfg(implies__dfg(v,w),x)))),
inference(sor,[status(thm)],[35,2]),
[iquote('0:SoR:35.0,2.0')] ).
cnf(474,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
| is_a_theorem(implies__dfg(implies__dfg(x,v),implies__dfg(u,implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[113,1]),
[iquote('0:Res:113.0,1.1')] ).
cnf(4008,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),x)),implies__dfg(implies__dfg(v,y),implies__dfg(u,implies__dfg(implies__dfg(y,w),x))))),
inference(sor,[status(thm)],[474,115]),
[iquote('0:SoR:474.0,115.0')] ).
cnf(4022,plain,
$false,
inference(unc,[status(thm)],[4008,5]),
[iquote('0:UnC:4008.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL358-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n016.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 02:58:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.95/1.24
% 0.95/1.24 SPASS V 3.9
% 0.95/1.24 SPASS beiseite: Proof found.
% 0.95/1.24 % SZS status Theorem
% 0.95/1.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.95/1.24 SPASS derived 3973 clauses, backtracked 0 clauses, performed 0 splits and kept 1514 clauses.
% 0.95/1.24 SPASS allocated 81478 KBytes.
% 0.95/1.24 SPASS spent 0:00:00.84 on the problem.
% 0.95/1.24 0:00:00.03 for the input.
% 0.95/1.24 0:00:00.00 for the FLOTTER CNF translation.
% 0.95/1.24 0:00:00.07 for inferences.
% 0.95/1.24 0:00:00.00 for the backtracking.
% 0.95/1.24 0:00:00.70 for the reduction.
% 0.95/1.24
% 0.95/1.24
% 0.95/1.24 Here is a proof with depth 6, length 11 :
% 0.95/1.24 % SZS output start Refutation
% See solution above
% 0.95/1.24 Formulae used in the proof : condensed_detachment cn_1 prove_cn_07
% 0.95/1.24
%------------------------------------------------------------------------------