%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 01:07:43 PM UTC 2026
% Result : Theorem 0.39s 0.69s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 16 ( 9 unt; 1 nHn; 16 RR)
% Number of literals : 26 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
modus_ponens,
file('LCL540+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL540+1.p',unknown),
[] ).
cnf(31,axiom,
~ adjunction,
file('LCL540+1.p',unknown),
[] ).
cnf(35,axiom,
is_a_theorem(skc153),
file('LCL540+1.p',unknown),
[] ).
cnf(37,axiom,
( is_a_theorem(skc152)
| adjunction ),
file('LCL540+1.p',unknown),
[] ).
cnf(44,axiom,
~ is_a_theorem(and__dfg(skc153,skc152)),
file('LCL540+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL540+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL540+1.p',unknown),
[] ).
cnf(148,plain,
is_a_theorem(skc152),
inference(mrr,[status(thm)],[37,31]),
[iquote('0:MRR:37.1,31.0')] ).
cnf(164,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[95,17]),
[iquote('0:MRR:95.0,17.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
cnf(190,plain,
( ~ is_a_theorem(implies__dfg(skc152,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[148,177]),
[iquote('0:Res:148.0,177.0')] ).
cnf(417,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,and__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[164,177]),
[iquote('0:Res:164.0,177.1')] ).
cnf(756,plain,
( ~ is_a_theorem(u)
| is_a_theorem(and__dfg(u,skc152)) ),
inference(res,[status(thm),theory(equality)],[417,190]),
[iquote('0:Res:417.1,190.0')] ).
cnf(760,plain,
~ is_a_theorem(skc153),
inference(res,[status(thm),theory(equality)],[756,44]),
[iquote('0:Res:756.1,44.0')] ).
cnf(761,plain,
$false,
inference(ssi,[status(thm)],[760,35]),
[iquote('0:SSi:760.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL540+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 16:04:04 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.39/0.69
% 0.39/0.69 SPASS V 3.9
% 0.39/0.69 SPASS beiseite: Proof found.
% 0.39/0.69 % SZS status Theorem
% 0.39/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.69 SPASS derived 500 clauses, backtracked 0 clauses, performed 2 splits and kept 408 clauses.
% 0.39/0.69 SPASS allocated 98687 KBytes.
% 0.39/0.69 SPASS spent 0:00:00.30 on the problem.
% 0.39/0.69 0:00:00.06 for the input.
% 0.39/0.69 0:00:00.08 for the FLOTTER CNF translation.
% 0.39/0.69 0:00:00.02 for inferences.
% 0.39/0.69 0:00:00.00 for the backtracking.
% 0.39/0.69 0:00:00.09 for the reduction.
% 0.39/0.69
% 0.39/0.69
% 0.39/0.69 Here is a proof with depth 3, length 16 :
% 0.39/0.69 % SZS output start Refutation
% See solution above
% 0.39/0.69 Formulae used in the proof : hilbert_modus_ponens hilbert_and_3 s1_0_adjunction adjunction and_3 modus_ponens
% 0.39/0.69
%------------------------------------------------------------------------------