%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 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 01:06:46 PM UTC 2026
% Result : Unsatisfiable 1.36s 1.65s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 13 RR)
% Number of literals : 18 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 14 ( 14 usr; 13 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('LCL098-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y),y)),
file('LCL098-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('LCL098-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),x)),y))
| is_a_theorem(y) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(equivalent(x,v),equivalent(equivalent(u,x),w)))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(equivalent(equivalent(w,x),equivalent(w,y)),u),equivalent(equivalent(x,y),v)))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(x,y),equivalent(x,z)),x1)),equivalent(equivalent(v,w),equivalent(equivalent(y,z),x1)))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(w,x),equivalent(w,y)),u),equivalent(equivalent(x,y),v))) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(equivalent(equivalent(x,y),equivalent(x,z)),x1),equivalent(equivalent(y,z),x1)),x2)),equivalent(equivalent(v,w),x2))),
inference(sor,[status(thm)],[15,2]),
[iquote('0:SoR:15.0,2.0')] ).
cnf(54,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),equivalent(equivalent(equivalent(x,y),equivalent(x,z)),x1)))
| is_a_theorem(equivalent(equivalent(v,w),equivalent(equivalent(y,z),x1))) ),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.1')] ).
cnf(464,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(u,v),equivalent(u,w)),x),equivalent(equivalent(v,w),y)),z),equivalent(equivalent(x,y),z))),
inference(sor,[status(thm)],[54,22]),
[iquote('0:SoR:54.0,22.0')] ).
cnf(1125,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(equivalent(equivalent(u,y),w),equivalent(equivalent(v,y),x)))),
inference(sor,[status(thm)],[7,464]),
[iquote('0:SoR:7.0,464.0')] ).
cnf(1135,plain,
$false,
inference(unc,[status(thm)],[1125,3]),
[iquote('0:UnC:1125.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 22:21:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 1.36/1.65
% 1.36/1.65 SPASS V 3.9
% 1.36/1.65 SPASS beiseite: Proof found.
% 1.36/1.65 % SZS status Theorem
% 1.36/1.65 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.36/1.65 SPASS derived 1128 clauses, backtracked 0 clauses, performed 0 splits and kept 1036 clauses.
% 1.36/1.65 SPASS allocated 81488 KBytes.
% 1.36/1.65 SPASS spent 0:00:01.18 on the problem.
% 1.36/1.65 0:00:00.06 for the input.
% 1.36/1.65 0:00:00.00 for the FLOTTER CNF translation.
% 1.36/1.65 0:00:00.07 for inferences.
% 1.36/1.65 0:00:00.00 for the backtracking.
% 1.36/1.65 0:00:01.00 for the reduction.
% 1.36/1.65
% 1.36/1.65
% 1.36/1.65 Here is a proof with depth 7, length 13 :
% 1.36/1.65 % SZS output start Refutation
% See solution above
% 1.36/1.65 Formulae used in the proof : condensed_detachment lg_3 prove_lg_4
% 1.36/1.65
%------------------------------------------------------------------------------