%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 01:06:50 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.50s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 5 unt; 0 nHn; 18 RR)
% Number of literals : 38 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 2 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('LCL126-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(u,equivalent(v,w)),equivalent(w,v)))),
file('LCL126-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(u,w),equivalent(v,w)))),
file('LCL126-1.p',unknown),
[] ).
cnf(4,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
file('LCL126-1.p',unknown),
[] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(u,equivalent(v,w)),equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| is_a_theorem(equivalent(w,v)) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.1,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(u,equivalent(v,w)))
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,w)) ),
inference(sor,[status(thm)],[14,10]),
[iquote('0:SoR:14.1,10.1')] ).
cnf(16,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,w),equivalent(u,equivalent(w,v)))) ),
inference(sor,[status(thm)],[14,2]),
[iquote('0:SoR:14.1,2.0')] ).
cnf(19,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(w)
| is_a_theorem(equivalent(equivalent(v,u),w)) ),
inference(sor,[status(thm)],[14,16]),
[iquote('0:SoR:14.1,16.1')] ).
cnf(20,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,w))
| is_a_theorem(equivalent(u,equivalent(w,v))) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.1,1.1')] ).
cnf(37,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,equivalent(w,x)),equivalent(x,w)),v),u)) ),
inference(sor,[status(thm)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(42,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(u,equivalent(equivalent(equivalent(v,equivalent(w,x)),equivalent(x,w)),v))) ),
inference(sor,[status(thm)],[20,2]),
[iquote('0:SoR:20.1,2.0')] ).
cnf(105,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,equivalent(v,w)),equivalent(w,v)),u))
| ~ is_a_theorem(equivalent(x,y))
| is_a_theorem(equivalent(y,x)) ),
inference(sor,[status(thm)],[14,37]),
[iquote('0:SoR:14.1,37.1')] ).
cnf(122,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(v,equivalent(w,x)),equivalent(x,w)),v)) ),
inference(sor,[status(thm)],[15,42]),
[iquote('0:SoR:15.0,42.1')] ).
cnf(126,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(v,equivalent(w,x)),equivalent(x,w)),v)) ),
inference(obv,[status(thm),theory(equality)],[122]),
[iquote('0:Obv:122.0')] ).
cnf(127,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(mrr,[status(thm)],[105,126]),
[iquote('0:MRR:105.0,126.1')] ).
cnf(142,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(w,v)),equivalent(u,w))),
inference(sor,[status(thm)],[127,3]),
[iquote('0:SoR:127.0,3.0')] ).
cnf(143,plain,
$false,
inference(unc,[status(thm)],[142,4]),
[iquote('0:UnC:142.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n004.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 10:59:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.23/0.50
% 0.23/0.50 SPASS V 3.9
% 0.23/0.50 SPASS beiseite: Proof found.
% 0.23/0.50 % SZS status Theorem
% 0.23/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.50 SPASS derived 131 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses.
% 0.23/0.50 SPASS allocated 75943 KBytes.
% 0.23/0.50 SPASS spent 0:00:00.12 on the problem.
% 0.23/0.50 0:00:00.06 for the input.
% 0.23/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.50 0:00:00.01 for inferences.
% 0.23/0.50 0:00:00.00 for the backtracking.
% 0.23/0.50 0:00:00.02 for the reduction.
% 0.23/0.50
% 0.23/0.50
% 0.23/0.50 Here is a proof with depth 7, length 18 :
% 0.23/0.50 % SZS output start Refutation
% See solution above
% 0.23/0.50 Formulae used in the proof : condensed_detachment q_3 q_4 prove_q_2
% 0.23/0.50
%------------------------------------------------------------------------------