%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 01:06:52 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 12 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ordered(x__dfg,y__dfg),
file('LCL143-1.p',unknown),
[] ).
cnf(2,axiom,
~ ordered(implies__dfg(z__dfg,x__dfg),implies__dfg(z__dfg,y__dfg)),
file('LCL143-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(truth,u),u),
file('LCL143-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL143-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ordered(u,v)
| equal(implies__dfg(u,v),truth) ),
file('LCL143-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(implies__dfg(u,v),truth)
| ordered(u,v) ),
file('LCL143-1.p',unknown),
[] ).
cnf(12,plain,
equal(implies__dfg(x__dfg,y__dfg),truth),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(131,plain,
equal(implies__dfg(implies__dfg(u,x__dfg),implies__dfg(truth,implies__dfg(u,y__dfg))),truth),
inference(spr,[status(thm),theory(equality)],[12,4]),
[iquote('0:SpR:12.0,4.0')] ).
cnf(154,plain,
equal(implies__dfg(implies__dfg(u,x__dfg),implies__dfg(u,y__dfg)),truth),
inference(rew,[status(thm),theory(equality)],[3,131]),
[iquote('0:Rew:3.0,131.0')] ).
cnf(396,plain,
( ~ equal(truth,truth)
| ordered(implies__dfg(u,x__dfg),implies__dfg(u,y__dfg)) ),
inference(spl,[status(thm),theory(equality)],[154,10]),
[iquote('0:SpL:154.0,10.0')] ).
cnf(404,plain,
ordered(implies__dfg(u,x__dfg),implies__dfg(u,y__dfg)),
inference(obv,[status(thm),theory(equality)],[396]),
[iquote('0:Obv:396.0')] ).
cnf(405,plain,
$false,
inference(unc,[status(thm)],[404,2]),
[iquote('0:UnC:404.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n031.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 23:47:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.22/0.51
% 0.22/0.51 SPASS V 3.9
% 0.22/0.51 SPASS beiseite: Proof found.
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 312 clauses, backtracked 0 clauses, performed 0 splits and kept 128 clauses.
% 0.22/0.51 SPASS allocated 63493 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.51 0:00:00.06 for the input.
% 0.22/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.00 for inferences.
% 0.22/0.51 0:00:00.00 for the backtracking.
% 0.22/0.51 0:00:00.02 for the reduction.
% 0.22/0.51
% 0.22/0.51
% 0.22/0.51 Here is a proof with depth 3, length 12 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : antecedent prove_wajsberg_theorem wajsberg_1 wajsberg_2 partial_order_definition1 partial_order_definition2
% 0.22/0.51
%------------------------------------------------------------------------------