%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 01:07:41 PM UTC 2026
% Result : Theorem 0.45s 0.70s
% Output : Refutation 0.45s
% 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('LCL527+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL527+1.p',unknown),
[] ).
cnf(30,axiom,
~ adjunction,
file('LCL527+1.p',unknown),
[] ).
cnf(34,axiom,
is_a_theorem(skc153),
file('LCL527+1.p',unknown),
[] ).
cnf(36,axiom,
( is_a_theorem(skc152)
| adjunction ),
file('LCL527+1.p',unknown),
[] ).
cnf(43,axiom,
~ is_a_theorem(and__dfg(skc153,skc152)),
file('LCL527+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL527+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL527+1.p',unknown),
[] ).
cnf(147,plain,
is_a_theorem(skc152),
inference(mrr,[status(thm)],[36,30]),
[iquote('0:MRR:36.1,30.0')] ).
cnf(162,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[94,17]),
[iquote('0:MRR:94.0,17.0')] ).
cnf(175,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[108,10]),
[iquote('0:MRR:108.1,10.0')] ).
cnf(188,plain,
( ~ is_a_theorem(implies__dfg(skc152,u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[147,175]),
[iquote('0:Res:147.0,175.0')] ).
cnf(425,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,and__dfg(u,v))) ),
inference(res,[status(thm),theory(equality)],[162,175]),
[iquote('0:Res:162.0,175.1')] ).
cnf(759,plain,
( ~ is_a_theorem(u)
| is_a_theorem(and__dfg(u,skc152)) ),
inference(res,[status(thm),theory(equality)],[425,188]),
[iquote('0:Res:425.1,188.0')] ).
cnf(764,plain,
~ is_a_theorem(skc153),
inference(res,[status(thm),theory(equality)],[759,43]),
[iquote('0:Res:759.1,43.0')] ).
cnf(765,plain,
$false,
inference(ssi,[status(thm)],[764,34]),
[iquote('0:SSi:764.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL527+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n011.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 : Sun Sep 6 00:37:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.45/0.70
% 0.45/0.70 SPASS V 3.9
% 0.45/0.70 SPASS beiseite: Proof found.
% 0.45/0.70 % SZS status Theorem
% 0.45/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.70 SPASS derived 503 clauses, backtracked 0 clauses, performed 2 splits and kept 412 clauses.
% 0.45/0.70 SPASS allocated 98686 KBytes.
% 0.45/0.70 SPASS spent 0:00:00.30 on the problem.
% 0.45/0.70 0:00:00.06 for the input.
% 0.45/0.70 0:00:00.08 for the FLOTTER CNF translation.
% 0.45/0.70 0:00:00.02 for inferences.
% 0.45/0.70 0:00:00.00 for the backtracking.
% 0.45/0.70 0:00:00.09 for the reduction.
% 0.45/0.70
% 0.45/0.70
% 0.45/0.70 Here is a proof with depth 3, length 16 :
% 0.45/0.70 % SZS output start Refutation
% See solution above
% 0.45/0.70 Formulae used in the proof : hilbert_modus_ponens hilbert_and_3 s1_0_adjunction adjunction and_3 modus_ponens
% 0.45/0.70
%------------------------------------------------------------------------------