%------------------------------------------------------------------------------
% 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 : n013.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 : Theorem 0.46s 0.66s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(x22__dfg(u,u),u),
file('SWX204+1.p',unknown),
[] ).
cnf(2,axiom,
equal(proj1S(s(u)),u),
file('SWX204+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(s(u),z__dfg),
file('SWX204+1.p',unknown),
[] ).
cnf(4,axiom,
equal(x2__dfg(z__dfg,u),u),
file('SWX204+1.p',unknown),
[] ).
cnf(5,axiom,
equal(x22__dfg(z__dfg,u),z__dfg),
file('SWX204+1.p',unknown),
[] ).
cnf(6,axiom,
equal(x2__dfg(s(u),v),s(x2__dfg(u,v))),
file('SWX204+1.p',unknown),
[] ).
cnf(7,axiom,
equal(x2__dfg(u,x22__dfg(v,u)),x22__dfg(s(v),u)),
file('SWX204+1.p',unknown),
[] ).
cnf(15,plain,
equal(s(x2__dfg(u,x22__dfg(v,s(u)))),x22__dfg(s(v),s(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(17,plain,
equal(x22__dfg(s(z__dfg),u),x2__dfg(u,z__dfg)),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(52,plain,
equal(x2__dfg(u,x22__dfg(v,s(u))),proj1S(x22__dfg(s(v),s(u)))),
inference(spr,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpR:15.0,2.0')] ).
cnf(139,plain,
equal(s(x2__dfg(u,x22__dfg(v,s(s(u))))),proj1S(x22__dfg(s(v),s(s(u))))),
inference(spr,[status(thm),theory(equality)],[52,6]),
[iquote('0:SpR:52.0,6.0')] ).
cnf(1357,plain,
equal(proj1S(x22__dfg(s(u),s(s(z__dfg)))),s(x22__dfg(u,s(s(z__dfg))))),
inference(spr,[status(thm),theory(equality)],[4,139]),
[iquote('0:SpR:4.0,139.0')] ).
cnf(1571,plain,
equal(s(x22__dfg(s(z__dfg),s(s(z__dfg)))),proj1S(s(s(z__dfg)))),
inference(spr,[status(thm),theory(equality)],[1,1357]),
[iquote('0:SpR:1.0,1357.0')] ).
cnf(1577,plain,
equal(s(s(s(z__dfg))),s(z__dfg)),
inference(rew,[status(thm),theory(equality)],[4,1571,6,17,2]),
[iquote('0:Rew:4.0,1571.0,6.0,1571.0,6.0,1571.0,17.0,1571.0,2.0,1571.0')] ).
cnf(1630,plain,
equal(proj1S(s(z__dfg)),s(s(z__dfg))),
inference(spr,[status(thm),theory(equality)],[1577,2]),
[iquote('0:SpR:1577.0,2.0')] ).
cnf(1759,plain,
equal(s(s(z__dfg)),z__dfg),
inference(rew,[status(thm),theory(equality)],[2,1630]),
[iquote('0:Rew:2.0,1630.0')] ).
cnf(1760,plain,
$false,
inference(mrr,[status(thm)],[1759,3]),
[iquote('0:MRR:1759.0,3.0')] ).
%------------------------------------------------------------------------------
%----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 : n013.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 11:28:10 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.46/0.66
% 0.46/0.66 SPASS V 3.9
% 0.46/0.66 SPASS beiseite: Proof found.
% 0.46/0.66 % SZS status Theorem
% 0.46/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.66 SPASS derived 1672 clauses, backtracked 0 clauses, performed 0 splits and kept 640 clauses.
% 0.46/0.66 SPASS allocated 88802 KBytes.
% 0.46/0.66 SPASS spent 0:00:00.29 on the problem.
% 0.46/0.66 0:00:00.03 for the input.
% 0.46/0.66 0:00:00.02 for the FLOTTER CNF translation.
% 0.46/0.66 0:00:00.02 for inferences.
% 0.46/0.66 0:00:00.00 for the backtracking.
% 0.46/0.66 0:00:00.19 for the reduction.
% 0.46/0.66
% 0.46/0.66
% 0.46/0.66 Here is a proof with depth 6, length 17 :
% 0.46/0.66 % SZS output start Refutation
% See solution above
% 0.46/0.66 Formulae used in the proof : goal_007 axiom_001 axiom_002 axiom_003 axiom_005 axiom_004 axiom_006
% 0.46/0.66
%------------------------------------------------------------------------------