%------------------------------------------------------------------------------
% 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 : Unsatisfiable 2.43s 2.62s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 33 RR)
% Number of literals : 33 ( 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 : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(44,axiom,
equal(d(n(u)),n(z__dfg)),
file('SWX190-1.p',unknown),
[] ).
cnf(45,axiom,
equal(x__dfg(d(u),d(v)),d(x__dfg(u,v))),
file('SWX190-1.p',unknown),
[] ).
cnf(47,axiom,
equal(n(s(z__dfg)),d(x2__dfg)),
file('SWX190-1.p',unknown),
[] ).
cnf(53,axiom,
equal(opt(x__dfg(n(z__dfg),u)),u),
file('SWX190-1.p',unknown),
[] ).
cnf(64,axiom,
equal(eq2(opt(d(u)),opt(d(opt(u)))),prop4(u)),
file('SWX190-1.p',unknown),
[] ).
cnf(75,axiom,
equal(eq2(x__dfg(u,v),n(w)),bfalse),
file('SWX190-1.p',unknown),
[] ).
cnf(89,axiom,
equal(eq3(u,u),btrue),
file('SWX190-1.p',unknown),
[] ).
cnf(90,axiom,
~ equal(eq3(prop4(u),bfalse),btrue),
file('SWX190-1.p',unknown),
[] ).
cnf(118,plain,
equal(d(d(x2__dfg)),n(z__dfg)),
inference(spr,[status(thm),theory(equality)],[47,44]),
[iquote('0:SpR:47.0,44.0')] ).
cnf(403,plain,
equal(eq2(d(x__dfg(u,v)),n(w)),bfalse),
inference(spr,[status(thm),theory(equality)],[45,75]),
[iquote('0:SpR:45.0,75.0')] ).
cnf(413,plain,
equal(x__dfg(d(u),n(z__dfg)),d(x__dfg(u,d(x2__dfg)))),
inference(spr,[status(thm),theory(equality)],[118,45]),
[iquote('0:SpR:118.0,45.0')] ).
cnf(414,plain,
equal(x__dfg(n(z__dfg),d(u)),d(x__dfg(n(v),u))),
inference(spr,[status(thm),theory(equality)],[44,45]),
[iquote('0:SpR:44.0,45.0')] ).
cnf(415,plain,
equal(x__dfg(n(z__dfg),d(u)),d(x__dfg(d(x2__dfg),u))),
inference(spr,[status(thm),theory(equality)],[118,45]),
[iquote('0:SpR:118.0,45.0')] ).
cnf(417,plain,
equal(d(x__dfg(d(x2__dfg),u)),d(x__dfg(n(v),u))),
inference(rew,[status(thm),theory(equality)],[415,414]),
[iquote('0:Rew:415.0,414.0')] ).
cnf(511,plain,
equal(eq2(opt(d(x__dfg(n(z__dfg),u))),opt(d(u))),prop4(x__dfg(n(z__dfg),u))),
inference(spr,[status(thm),theory(equality)],[53,64]),
[iquote('0:SpR:53.0,64.0')] ).
cnf(639,plain,
equal(eq2(d(d(x__dfg(u,v))),n(w)),bfalse),
inference(spr,[status(thm),theory(equality)],[45,403]),
[iquote('0:SpR:45.0,403.0')] ).
cnf(838,plain,
equal(eq2(d(d(d(x__dfg(u,v)))),n(w)),bfalse),
inference(spr,[status(thm),theory(equality)],[45,639]),
[iquote('0:SpR:45.0,639.0')] ).
cnf(1322,plain,
equal(d(x__dfg(d(x2__dfg),d(x2__dfg))),x__dfg(n(z__dfg),n(z__dfg))),
inference(spr,[status(thm),theory(equality)],[118,413]),
[iquote('0:SpR:118.0,413.0')] ).
cnf(1326,plain,
equal(x__dfg(n(z__dfg),n(z__dfg)),d(d(x__dfg(x2__dfg,x2__dfg)))),
inference(rew,[status(thm),theory(equality)],[45,1322]),
[iquote('0:Rew:45.0,1322.0')] ).
cnf(1552,plain,
equal(opt(d(x__dfg(d(x2__dfg),u))),d(u)),
inference(spr,[status(thm),theory(equality)],[415,53]),
[iquote('0:SpR:415.0,53.0')] ).
cnf(2839,plain,
equal(opt(d(x__dfg(n(u),v))),d(v)),
inference(spr,[status(thm),theory(equality)],[417,1552]),
[iquote('0:SpR:417.0,1552.0')] ).
cnf(2889,plain,
equal(eq2(d(u),opt(d(u))),prop4(x__dfg(n(z__dfg),u))),
inference(rew,[status(thm),theory(equality)],[2839,511]),
[iquote('0:Rew:2839.0,511.0')] ).
cnf(2920,plain,
equal(opt(d(d(x__dfg(d(x2__dfg),u)))),d(d(u))),
inference(spr,[status(thm),theory(equality)],[415,2839]),
[iquote('0:SpR:415.0,2839.0')] ).
cnf(4196,plain,
equal(opt(d(d(x__dfg(n(u),v)))),d(d(v))),
inference(spr,[status(thm),theory(equality)],[417,2920]),
[iquote('0:SpR:417.0,2920.0')] ).
cnf(5514,plain,
equal(eq2(d(d(d(d(x__dfg(u,v))))),n(w)),bfalse),
inference(spr,[status(thm),theory(equality)],[45,838]),
[iquote('0:SpR:45.0,838.0')] ).
cnf(12028,plain,
equal(opt(d(d(d(d(x__dfg(x2__dfg,x2__dfg)))))),d(d(n(z__dfg)))),
inference(spr,[status(thm),theory(equality)],[1326,4196]),
[iquote('0:SpR:1326.0,4196.0')] ).
cnf(12033,plain,
equal(opt(d(d(d(d(x__dfg(x2__dfg,x2__dfg)))))),n(z__dfg)),
inference(rew,[status(thm),theory(equality)],[44,12028]),
[iquote('0:Rew:44.0,12028.0,44.0,12028.0')] ).
cnf(12095,plain,
equal(eq2(d(d(d(d(x__dfg(x2__dfg,x2__dfg))))),n(z__dfg)),prop4(x__dfg(n(z__dfg),d(d(d(x__dfg(x2__dfg,x2__dfg))))))),
inference(spr,[status(thm),theory(equality)],[12033,2889]),
[iquote('0:SpR:12033.0,2889.0')] ).
cnf(12134,plain,
equal(eq2(d(d(d(d(x__dfg(x2__dfg,x2__dfg))))),n(z__dfg)),prop4(d(d(x__dfg(x2__dfg,d(x__dfg(x2__dfg,x2__dfg))))))),
inference(rew,[status(thm),theory(equality)],[45,12095,415]),
[iquote('0:Rew:45.0,12095.0,415.0,12095.0')] ).
cnf(12135,plain,
equal(prop4(d(d(x__dfg(x2__dfg,d(x__dfg(x2__dfg,x2__dfg)))))),bfalse),
inference(rew,[status(thm),theory(equality)],[5514,12134]),
[iquote('0:Rew:5514.0,12134.0')] ).
cnf(12138,plain,
~ equal(eq3(bfalse,bfalse),btrue),
inference(spl,[status(thm),theory(equality)],[12135,90]),
[iquote('0:SpL:12135.0,90.0')] ).
cnf(12139,plain,
~ equal(btrue,btrue),
inference(rew,[status(thm),theory(equality)],[89,12138]),
[iquote('0:Rew:89.0,12138.0')] ).
cnf(12140,plain,
$false,
inference(obv,[status(thm),theory(equality)],[12139]),
[iquote('0:Obv:12139.0')] ).
%------------------------------------------------------------------------------
%----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
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 5 04:57:56 EDT 2026
% 0.06/0.25 % CPUTime :
% 2.43/2.62
% 2.43/2.62 SPASS V 3.9
% 2.43/2.62 SPASS beiseite: Proof found.
% 2.43/2.62 % SZS status Theorem
% 2.43/2.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.43/2.62 SPASS derived 10820 clauses, backtracked 0 clauses, performed 0 splits and kept 3492 clauses.
% 2.43/2.62 SPASS allocated 77053 KBytes.
% 2.43/2.62 SPASS spent 0:00:02.26 on the problem.
% 2.43/2.62 0:00:00.02 for the input.
% 2.43/2.62 0:00:00.00 for the FLOTTER CNF translation.
% 2.43/2.62 0:00:00.11 for inferences.
% 2.43/2.62 0:00:00.00 for the backtracking.
% 2.43/2.62 0:00:02.07 for the reduction.
% 2.43/2.62
% 2.43/2.62
% 2.43/2.62 Here is a proof with depth 9, length 33 :
% 2.43/2.62 % SZS output start Refutation
% See solution above
% 2.43/2.62 Formulae used in the proof : axiom_043 axiom_044 axiom_046 axiom_052 axiom_063 axiom_074 axiom_088 goal
% 2.43/2.62
%------------------------------------------------------------------------------