%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.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 01:06:46 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 18 RR)
% Number of literals : 26 ( 0 equ; 9 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 : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL104-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),u))),
file('LCL104-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,u),w)),w)),
file('LCL104-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('LCL104-1.p',unknown),
[] ).
cnf(9,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(v,u),w)))
| is_a_theorem(w) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(10,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v)))),
inference(sor,[status(thm)],[9,2]),
[iquote('0:SoR:9.0,2.0')] ).
cnf(11,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),equivalent(v,x)),equivalent(w,x)),u)) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(13,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(w,u),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.0,1.1')] ).
cnf(15,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(u,equivalent(equivalent(x,v),equivalent(x,w))))),
inference(sor,[status(thm)],[13,10]),
[iquote('0:SoR:13.0,10.0')] ).
cnf(16,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),x))),equivalent(u,x))),
inference(sor,[status(thm)],[13,3]),
[iquote('0:SoR:13.0,3.0')] ).
cnf(25,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,v),x))))
| is_a_theorem(equivalent(u,x)) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.0,1.1')] ).
cnf(47,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(v,w))),
inference(sor,[status(thm)],[25,15]),
[iquote('0:SoR:25.0,15.0')] ).
cnf(52,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(w,u),equivalent(w,v))),x),x)),
inference(sor,[status(thm)],[25,2]),
[iquote('0:SoR:25.0,2.0')] ).
cnf(56,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(u,w)))
| is_a_theorem(equivalent(v,w)) ),
inference(res,[status(thm),theory(equality)],[47,1]),
[iquote('0:Res:47.0,1.1')] ).
cnf(60,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x))
| is_a_theorem(equivalent(equivalent(v,w),x)) ),
inference(sor,[status(thm)],[56,11]),
[iquote('0:SoR:56.0,11.1')] ).
cnf(140,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x))),
inference(sor,[status(thm)],[60,52]),
[iquote('0:SoR:60.0,52.0')] ).
cnf(193,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[60,140]),
[iquote('0:SoR:60.0,140.0')] ).
cnf(195,plain,
$false,
inference(unc,[status(thm)],[193,4]),
[iquote('0:UnC:193.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n002.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 01:49:50 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.22/0.53
% 0.22/0.53 SPASS V 3.9
% 0.22/0.53 SPASS beiseite: Proof found.
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.53 SPASS derived 186 clauses, backtracked 0 clauses, performed 0 splits and kept 128 clauses.
% 0.22/0.53 SPASS allocated 76218 KBytes.
% 0.22/0.53 SPASS spent 0:00:00.15 on the problem.
% 0.22/0.53 0:00:00.06 for the input.
% 0.22/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.53 0:00:00.01 for inferences.
% 0.22/0.53 0:00:00.00 for the backtracking.
% 0.22/0.53 0:00:00.04 for the reduction.
% 0.22/0.53
% 0.22/0.53
% 0.22/0.53 Here is a proof with depth 10, length 18 :
% 0.22/0.53 % SZS output start Refutation
% See solution above
% 0.22/0.53 Formulae used in the proof : condensed_detachment p_4 q_3 prove_p_1
% 0.22/0.53
%------------------------------------------------------------------------------