%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 07:07:24 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(x2__dfg(z__dfg,u),u),
file('SWX204-1.p',unknown),
[] ).
cnf(2,axiom,
equal(x2__dfg(s(u),v),s(x2__dfg(u,v))),
file('SWX204-1.p',unknown),
[] ).
cnf(3,axiom,
equal(x22__dfg(z__dfg,u),z__dfg),
file('SWX204-1.p',unknown),
[] ).
cnf(4,axiom,
equal(x2__dfg(u,x22__dfg(v,u)),x22__dfg(s(v),u)),
file('SWX204-1.p',unknown),
[] ).
cnf(5,axiom,
equal(eq(x22__dfg(u,u),u),mul_idem(u)),
file('SWX204-1.p',unknown),
[] ).
cnf(8,axiom,
equal(eq(s(u),s(v)),eq(u,v)),
file('SWX204-1.p',unknown),
[] ).
cnf(10,axiom,
equal(eq(s(u),z__dfg),bfalse),
file('SWX204-1.p',unknown),
[] ).
cnf(12,axiom,
equal(eq2(u,u),btrue),
file('SWX204-1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(eq2(mul_idem(u),bfalse),btrue),
file('SWX204-1.p',unknown),
[] ).
cnf(32,plain,
equal(s(x2__dfg(u,x22__dfg(v,s(u)))),x22__dfg(s(v),s(u))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(34,plain,
equal(x22__dfg(s(z__dfg),u),x2__dfg(u,z__dfg)),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(67,plain,
equal(s(s(x2__dfg(u,x22__dfg(v,s(s(u)))))),x22__dfg(s(v),s(s(u)))),
inference(spr,[status(thm),theory(equality)],[2,32]),
[iquote('0:SpR:2.0,32.0')] ).
cnf(176,plain,
equal(s(s(x22__dfg(u,s(s(z__dfg))))),x22__dfg(s(u),s(s(z__dfg)))),
inference(spr,[status(thm),theory(equality)],[1,67]),
[iquote('0:SpR:1.0,67.0')] ).
cnf(233,plain,
equal(x22__dfg(s(s(z__dfg)),s(s(z__dfg))),s(s(x2__dfg(s(s(z__dfg)),z__dfg)))),
inference(spr,[status(thm),theory(equality)],[34,176]),
[iquote('0:SpR:34.0,176.0')] ).
cnf(235,plain,
equal(x22__dfg(s(s(z__dfg)),s(s(z__dfg))),s(s(s(s(z__dfg))))),
inference(rew,[status(thm),theory(equality)],[1,233,2]),
[iquote('0:Rew:1.0,233.0,2.0,233.0,2.0,233.0')] ).
cnf(245,plain,
equal(eq(s(s(s(s(z__dfg)))),s(s(z__dfg))),mul_idem(s(s(z__dfg)))),
inference(spr,[status(thm),theory(equality)],[235,5]),
[iquote('0:SpR:235.0,5.0')] ).
cnf(262,plain,
equal(mul_idem(s(s(z__dfg))),bfalse),
inference(rew,[status(thm),theory(equality)],[10,245,8]),
[iquote('0:Rew:10.0,245.0,8.0,245.0,8.0,245.0')] ).
cnf(270,plain,
~ equal(eq2(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[262,13]),
[iquote('0:SpL:262.0,13.0')] ).
cnf(271,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[12,270]),
[iquote('0:Rew:12.0,270.0')] ).
cnf(272,plain,
$false,
inference(obv,[status(thm),theory(equality)],[271]),
[iquote('0:Obv:271.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 11:28:53 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 192 clauses, backtracked 0 clauses, performed 0 splits and kept 71 clauses.
% 0.19/0.44 SPASS allocated 63538 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.02 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 6, length 20 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : axiom axiom_001 axiom_002 axiom_003 axiom_004 axiom_007 axiom_009 axiom_011 goal
% 0.19/0.44
%------------------------------------------------------------------------------