%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL110-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 01:06:48 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 12 unt; 0 nHn; 24 RR)
% Number of literals : 38 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 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('LCL110-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL110-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL110-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u))),
file('LCL110-1.p',unknown),
[] ).
cnf(5,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL110-1.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(not__dfg(not__dfg(a)),a)),
file('LCL110-1.p',unknown),
[] ).
cnf(13,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),v))
| is_a_theorem(implies__dfg(implies__dfg(v,u),u)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(19,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)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[15,13]),
[iquote('0:SoR:15.0,13.1')] ).
cnf(22,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.1,1.1')] ).
cnf(33,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(not__dfg(v),not__dfg(u)),w))),
inference(sor,[status(thm)],[19,5]),
[iquote('0:SoR:19.0,5.0')] ).
cnf(34,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(36,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(v,w)) ),
inference(sor,[status(thm)],[22,34]),
[iquote('0:SoR:22.1,34.0')] ).
cnf(42,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(sor,[status(thm)],[36,20]),
[iquote('0:SoR:36.0,20.1')] ).
cnf(47,plain,
is_a_theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
inference(sor,[status(thm)],[36,5]),
[iquote('0:SoR:36.0,5.0')] ).
cnf(51,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[42,34]),
[iquote('0:EmS:42.0,34.0')] ).
cnf(63,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(v),not__dfg(u)),w)) ),
inference(sor,[status(thm)],[22,33]),
[iquote('0:SoR:22.1,33.0')] ).
cnf(66,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(not__dfg(u),w))),
inference(sor,[status(thm)],[19,47]),
[iquote('0:SoR:19.0,47.0')] ).
cnf(101,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
| is_a_theorem(implies__dfg(not__dfg(u),w)) ),
inference(sor,[status(thm)],[22,66]),
[iquote('0:SoR:22.1,66.0')] ).
cnf(355,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(not__dfg(v),not__dfg(u)),v)) ),
inference(sor,[status(thm)],[63,20]),
[iquote('0:SoR:63.0,20.1')] ).
cnf(389,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(not__dfg(not__dfg(v)),v)) ),
inference(sor,[status(thm)],[101,355]),
[iquote('0:SoR:101.0,355.1')] ).
cnf(394,plain,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
inference(ems,[status(thm)],[389,51]),
[iquote('0:EmS:389.0,51.0')] ).
cnf(436,plain,
$false,
inference(unc,[status(thm)],[394,6]),
[iquote('0:UnC:394.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL110-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 21:41:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.21/0.55
% 0.21/0.55 SPASS V 3.9
% 0.21/0.55 SPASS beiseite: Proof found.
% 0.21/0.55 % SZS status Theorem
% 0.21/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.55 SPASS derived 409 clauses, backtracked 0 clauses, performed 0 splits and kept 250 clauses.
% 0.21/0.55 SPASS allocated 76200 KBytes.
% 0.21/0.55 SPASS spent 0:00:00.17 on the problem.
% 0.21/0.55 0:00:00.06 for the input.
% 0.21/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.55 0:00:00.01 for inferences.
% 0.21/0.55 0:00:00.00 for the backtracking.
% 0.21/0.55 0:00:00.05 for the reduction.
% 0.21/0.55
% 0.21/0.55
% 0.21/0.55 Here is a proof with depth 9, length 24 :
% 0.21/0.55 % SZS output start Refutation
% See solution above
% 0.21/0.55 Formulae used in the proof : condensed_detachment mv_1 mv_2 mv_3 mv_5 prove_mv_24
% 0.21/0.55
%------------------------------------------------------------------------------