%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL111-2 : 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 01:06:48 PM UTC 2026
% Result : Unsatisfiable 2.95s 3.28s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(implies__dfg(implies__dfg(x__dfg,y__dfg),implies__dfg(implies__dfg(z__dfg,x__dfg),implies__dfg(z__dfg,y__dfg))),truth),
file('LCL111-2.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL111-2.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL111-2.p',unknown),
[] ).
cnf(25,plain,
equal(implies__dfg(truth,implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),truth),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(28,plain,
equal(implies__dfg(implies__dfg(truth,u),implies__dfg(implies__dfg(u,v),v)),truth),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(45,plain,
equal(implies__dfg(u,implies__dfg(implies__dfg(u,v),v)),truth),
inference(rew,[status(thm),theory(equality)],[2,28]),
[iquote('0:Rew:2.0,28.0')] ).
cnf(51,plain,
equal(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x)),truth),
inference(rew,[status(thm),theory(equality)],[2,25]),
[iquote('0:Rew:2.0,25.0')] ).
cnf(149,plain,
equal(implies__dfg(truth,implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),v),w),implies__dfg(u,w))),truth),
inference(spr,[status(thm),theory(equality)],[45,3]),
[iquote('0:SpR:45.0,3.0')] ).
cnf(216,plain,
equal(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),v),w),implies__dfg(u,w)),truth),
inference(rew,[status(thm),theory(equality)],[2,149]),
[iquote('0:Rew:2.0,149.0')] ).
cnf(7367,plain,
equal(implies__dfg(truth,implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),truth),
inference(spr,[status(thm),theory(equality)],[51,216]),
[iquote('0:SpR:51.0,216.0')] ).
cnf(7430,plain,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v))),truth),
inference(rew,[status(thm),theory(equality)],[2,7367]),
[iquote('0:Rew:2.0,7367.0')] ).
cnf(7431,plain,
$false,
inference(unc,[status(thm)],[7430,1]),
[iquote('0:UnC:7430.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL111-2 : 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
% 0.11/0.36 % DateTime : Sat Sep 5 09:06:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 2.95/3.28
% 2.95/3.28 SPASS V 3.9
% 2.95/3.28 SPASS beiseite: Proof found.
% 2.95/3.28 % SZS status Theorem
% 2.95/3.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.95/3.28 SPASS derived 4846 clauses, backtracked 0 clauses, performed 0 splits and kept 979 clauses.
% 2.95/3.28 SPASS allocated 72678 KBytes.
% 2.95/3.28 SPASS spent 0:00:02.77 on the problem.
% 2.95/3.28 0:00:00.06 for the input.
% 2.95/3.28 0:00:00.00 for the FLOTTER CNF translation.
% 2.95/3.28 0:00:00.07 for inferences.
% 2.95/3.28 0:00:00.00 for the backtracking.
% 2.95/3.28 0:00:02.60 for the reduction.
% 2.95/3.28
% 2.95/3.28
% 2.95/3.28 Here is a proof with depth 3, length 12 :
% 2.95/3.28 % SZS output start Refutation
% See solution above
% 2.95/3.28 Formulae used in the proof : prove_mv_25 wajsberg_1 wajsberg_2
% 2.95/3.28
%------------------------------------------------------------------------------