%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:07:22 PM UTC 2026
% Result : Theorem 0.07s 0.32s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
equal(proj1(x__dfg(u,v)),u),
file('SWX190+1.p',unknown),
[] ).
cnf(14,axiom,
equal(d(n(u)),n(z__dfg)),
file('SWX190+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(n(u),x__dfg(v,w)),
file('SWX190+1.p',unknown),
[] ).
cnf(21,axiom,
equal(opt(x__dfg(n(z__dfg),u)),u),
file('SWX190+1.p',unknown),
[] ).
cnf(22,axiom,
equal(opt(d(opt(u))),opt(d(u))),
file('SWX190+1.p',unknown),
[] ).
cnf(31,axiom,
equal(x__dfg(d(u),d(v)),d(x__dfg(u,v))),
file('SWX190+1.p',unknown),
[] ).
cnf(82,plain,
equal(opt(d(x__dfg(n(z__dfg),u))),opt(d(u))),
inference(spr,[status(thm),theory(equality)],[21,22]),
[iquote('0:SpR:21.0,22.0')] ).
cnf(153,plain,
equal(proj1(d(x__dfg(u,v))),d(u)),
inference(spr,[status(thm),theory(equality)],[31,7]),
[iquote('0:SpR:31.0,7.0')] ).
cnf(157,plain,
equal(d(x__dfg(n(u),v)),x__dfg(n(z__dfg),d(v))),
inference(spr,[status(thm),theory(equality)],[14,31]),
[iquote('0:SpR:14.0,31.0')] ).
cnf(162,plain,
~ equal(n(u),d(x__dfg(v,w))),
inference(spl,[status(thm),theory(equality)],[31,16]),
[iquote('0:SpL:31.0,16.0')] ).
cnf(163,plain,
equal(opt(x__dfg(n(z__dfg),d(u))),opt(d(u))),
inference(rew,[status(thm),theory(equality)],[157,82]),
[iquote('0:Rew:157.0,82.0')] ).
cnf(168,plain,
equal(opt(d(u)),d(u)),
inference(rew,[status(thm),theory(equality)],[21,163]),
[iquote('0:Rew:21.0,163.0')] ).
cnf(171,plain,
equal(opt(d(u)),d(opt(u))),
inference(rew,[status(thm),theory(equality)],[168,22]),
[iquote('0:Rew:168.0,22.0')] ).
cnf(176,plain,
equal(d(opt(u)),d(u)),
inference(rew,[status(thm),theory(equality)],[168,171]),
[iquote('0:Rew:168.0,171.0')] ).
cnf(211,plain,
equal(d(x__dfg(n(z__dfg),u)),d(u)),
inference(spr,[status(thm),theory(equality)],[21,176]),
[iquote('0:SpR:21.0,176.0')] ).
cnf(215,plain,
equal(x__dfg(n(z__dfg),d(u)),d(u)),
inference(rew,[status(thm),theory(equality)],[157,211]),
[iquote('0:Rew:157.0,211.0')] ).
cnf(236,plain,
equal(proj1(d(u)),n(z__dfg)),
inference(spr,[status(thm),theory(equality)],[215,7]),
[iquote('0:SpR:215.0,7.0')] ).
cnf(249,plain,
equal(d(u),n(z__dfg)),
inference(rew,[status(thm),theory(equality)],[236,153]),
[iquote('0:Rew:236.0,153.0')] ).
cnf(250,plain,
$false,
inference(unc,[status(thm)],[249,162]),
[iquote('0:UnC:249.0,162.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : run_spass %d %s
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 04:53:26 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.32
% 0.07/0.32 SPASS V 3.9
% 0.07/0.32 SPASS beiseite: Proof found.
% 0.07/0.32 % SZS status Theorem
% 0.07/0.32 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.32 SPASS derived 157 clauses, backtracked 0 clauses, performed 0 splits and kept 141 clauses.
% 0.07/0.32 SPASS allocated 85369 KBytes.
% 0.07/0.32 SPASS spent 0:00:00.07 on the problem.
% 0.07/0.32 0:00:00.02 for the input.
% 0.07/0.32 0:00:00.02 for the FLOTTER CNF translation.
% 0.07/0.32 0:00:00.00 for inferences.
% 0.07/0.32 0:00:00.00 for the backtracking.
% 0.07/0.32 0:00:00.01 for the reduction.
% 0.07/0.32
% 0.07/0.32
% 0.07/0.32 Here is a proof with depth 2, length 19 :
% 0.07/0.32 % SZS output start Refutation
% See solution above
% 0.07/0.32 Formulae used in the proof : axiom_004 axiom_039 axiom_008 axiom_050 goal_054 axiom_040
% 0.07/0.32
%------------------------------------------------------------------------------