%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% 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 01:08:47 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% 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 : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 16 ( 16 usr; 14 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('LCL982+1.p',unknown),
[] ).
cnf(2,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(skc5,skc4),implies__dfg(implies__dfg(skc4,skc3),implies__dfg(skc5,skc3)))),
file('LCL982+1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(w,implies__dfg(x,y)),implies__dfg(v,implies__dfg(not__dfg(x),not__dfg(u)))),implies__dfg(u,x)))),
file('LCL982+1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(w,implies__dfg(x,y)),implies__dfg(v,implies__dfg(not__dfg(x),not__dfg(u)))),implies__dfg(u,x))) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(implies__dfg(implies__dfg(x,implies__dfg(y,z)),implies__dfg(x1,implies__dfg(not__dfg(y),not__dfg(x2)))),implies__dfg(x2,y)),implies__dfg(not__dfg(v),not__dfg(implies__dfg(x2,x1))))),implies__dfg(implies__dfg(x2,x1),v))),
inference(sor,[status(thm)],[7,3]),
[iquote('0:SoR:7.0,3.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(implies__dfg(x,y),z),implies__dfg(not__dfg(v),not__dfg(implies__dfg(implies__dfg(x1,implies__dfg(z,x2)),implies__dfg(implies__dfg(implies__dfg(implies__dfg(x3,implies__dfg(x4,x5)),implies__dfg(y,implies__dfg(not__dfg(x4),not__dfg(x)))),implies__dfg(x,x4)),implies__dfg(not__dfg(z),not__dfg(implies__dfg(x,y))))))))),implies__dfg(implies__dfg(implies__dfg(x1,implies__dfg(z,x2)),implies__dfg(implies__dfg(implies__dfg(implies__dfg(x3,implies__dfg(x4,x5)),implies__dfg(y,implies__dfg(not__dfg(x4),not__dfg(x)))),implies__dfg(x,x4)),implies__dfg(not__dfg(z),not__dfg(implies__dfg(x,y))))),v))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(implies__dfg(implies__dfg(x,implies__dfg(y,z)),implies__dfg(x1,implies__dfg(not__dfg(y),not__dfg(x2)))),implies__dfg(x2,y)),implies__dfg(not__dfg(v),not__dfg(implies__dfg(x2,x1))))))
| is_a_theorem(implies__dfg(implies__dfg(x2,x1),v)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(23,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,implies__dfg(not__dfg(v),not__dfg(y)))),implies__dfg(y,v)),z),implies__dfg(implies__dfg(y,x),z))),
inference(sor,[status(thm)],[10,9]),
[iquote('0:SoR:10.0,9.0')] ).
cnf(27,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,implies__dfg(not__dfg(v),not__dfg(y)))),implies__dfg(y,v)),z))
| is_a_theorem(implies__dfg(implies__dfg(y,x),z)) ),
inference(res,[status(thm),theory(equality)],[23,1]),
[iquote('0:Res:23.0,1.1')] ).
cnf(28,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(sor,[status(thm)],[27,23]),
[iquote('0:SoR:27.0,23.0')] ).
cnf(34,plain,
$false,
inference(unc,[status(thm)],[28,2]),
[iquote('0:UnC:28.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n014.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 : Sat Sep 5 16:13:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.45
% 0.13/0.45 SPASS V 3.9
% 0.13/0.45 SPASS beiseite: Proof found.
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.13/0.45 SPASS allocated 98255 KBytes.
% 0.13/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.13/0.45 0:00:00.03 for the input.
% 0.13/0.45 0:00:00.02 for the FLOTTER CNF translation.
% 0.13/0.45 0:00:00.00 for inferences.
% 0.13/0.45 0:00:00.00 for the backtracking.
% 0.13/0.45 0:00:00.00 for the reduction.
% 0.13/0.45
% 0.13/0.45
% 0.13/0.45 Here is a proof with depth 6, length 11 :
% 0.13/0.45 % SZS output start Refutation
% See solution above
% 0.13/0.45 Formulae used in the proof : condensed_detachment prove_cn_1 a5
% 0.13/0.45
%------------------------------------------------------------------------------