%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 14.44s 14.60s
% Output : Refutation 14.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 17 unt; 4 nHn; 29 RR)
% Number of literals : 56 ( 0 equ; 26 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(length(nil),z__dfg),
file('SWX187+1.p',unknown),
[] ).
cnf(2,axiom,
x2__dfg(z__dfg,s(u)),
file('SWX187+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(s(u),z__dfg),
file('SWX187+1.p',unknown),
[] ).
cnf(7,axiom,
equal(x__dfg(nil,u),u),
file('SWX187+1.p',unknown),
[] ).
cnf(8,axiom,
equal(rotate(z__dfg,u),u),
file('SWX187+1.p',unknown),
[] ).
cnf(9,axiom,
equal(head(cons(u,v)),u),
file('SWX187+1.p',unknown),
[] ).
cnf(13,axiom,
equal(length(cons(u,v)),s(length(v))),
file('SWX187+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ x2__dfg(u,v)
| x2__dfg(s(u),s(v)) ),
file('SWX187+1.p',unknown),
[] ).
cnf(16,axiom,
equal(x__dfg(cons(u,v),w),cons(u,x__dfg(v,w))),
file('SWX187+1.p',unknown),
[] ).
cnf(17,axiom,
equal(rotate(u,x__dfg(v,cons(w,nil))),rotate(s(u),cons(w,v))),
file('SWX187+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ x2__dfg(u,length(v))
| ~ x2__dfg(w,length(v))
| ~ equal(rotate(w,v),rotate(u,v))
| equal(w,u)
| equal(rotate(s(z__dfg),v),v) ),
file('SWX187+1.p',unknown),
[] ).
cnf(35,plain,
equal(rotate(s(z__dfg),cons(u,v)),x__dfg(v,cons(u,nil))),
inference(spr,[status(thm),theory(equality)],[17,8]),
[iquote('0:SpR:17.0,8.0')] ).
cnf(38,plain,
equal(rotate(u,cons(v,x__dfg(w,cons(x,nil)))),rotate(s(u),cons(x,cons(v,w)))),
inference(spr,[status(thm),theory(equality)],[16,17]),
[iquote('0:SpR:16.0,17.0')] ).
cnf(49,plain,
( ~ x2__dfg(z__dfg,length(u))
| ~ x2__dfg(v,length(u))
| ~ equal(rotate(v,u),u)
| equal(v,z__dfg)
| equal(rotate(s(z__dfg),u),u) ),
inference(spl,[status(thm),theory(equality)],[8,18]),
[iquote('0:SpL:8.0,18.2')] ).
cnf(64,plain,
equal(rotate(u,cons(v,cons(w,x__dfg(x,cons(y,nil))))),rotate(s(u),cons(y,cons(v,cons(w,x))))),
inference(spr,[status(thm),theory(equality)],[16,38]),
[iquote('0:SpR:16.0,38.0')] ).
cnf(91,plain,
equal(rotate(u,cons(v,cons(w,cons(x,x__dfg(y,cons(z,nil)))))),rotate(s(u),cons(z,cons(v,cons(w,cons(x,y)))))),
inference(spr,[status(thm),theory(equality)],[16,64]),
[iquote('0:SpR:16.0,64.0')] ).
cnf(155,plain,
equal(rotate(s(u),cons(v,cons(w,cons(x,cons(y,nil))))),rotate(u,cons(w,cons(x,cons(y,cons(v,nil)))))),
inference(spr,[status(thm),theory(equality)],[7,91]),
[iquote('0:SpR:7.0,91.0')] ).
cnf(177,plain,
( ~ x2__dfg(z__dfg,length(cons(u,cons(v,cons(w,cons(x,nil))))))
| ~ x2__dfg(s(y),length(cons(u,cons(v,cons(w,cons(x,nil))))))
| ~ equal(rotate(y,cons(v,cons(w,cons(x,cons(u,nil))))),cons(u,cons(v,cons(w,cons(x,nil)))))
| equal(s(y),z__dfg)
| equal(rotate(s(z__dfg),cons(u,cons(v,cons(w,cons(x,nil))))),cons(u,cons(v,cons(w,cons(x,nil))))) ),
inference(spl,[status(thm),theory(equality)],[155,49]),
[iquote('0:SpL:155.0,49.2')] ).
cnf(182,plain,
( ~ x2__dfg(z__dfg,s(s(s(s(z__dfg)))))
| ~ x2__dfg(s(u),s(s(s(s(z__dfg)))))
| ~ equal(rotate(u,cons(v,cons(w,cons(x,cons(y,nil))))),cons(y,cons(v,cons(w,cons(x,nil)))))
| equal(s(u),z__dfg)
| equal(cons(v,cons(w,cons(x,cons(y,nil)))),cons(y,cons(v,cons(w,cons(x,nil))))) ),
inference(rew,[status(thm),theory(equality)],[7,177,16,35,1,13]),
[iquote('0:Rew:7.0,177.4,16.0,177.4,16.0,177.4,16.0,177.4,35.0,177.4,1.0,177.1,13.0,177.1,13.0,177.1,13.0,177.1,13.0,177.1,1.0,177.0,13.0,177.0,13.0,177.0,13.0,177.0,13.0,177.0')] ).
cnf(183,plain,
( ~ x2__dfg(s(u),s(s(s(s(z__dfg)))))
| ~ equal(rotate(u,cons(v,cons(w,cons(x,cons(y,nil))))),cons(y,cons(v,cons(w,cons(x,nil)))))
| equal(cons(v,cons(w,cons(x,cons(y,nil)))),cons(y,cons(v,cons(w,cons(x,nil))))) ),
inference(mrr,[status(thm)],[182,2,5]),
[iquote('0:MRR:182.0,182.3,2.0,5.0')] ).
cnf(6808,plain,
( ~ x2__dfg(s(s(z__dfg)),s(s(s(s(z__dfg)))))
| ~ equal(x__dfg(cons(u,cons(v,cons(w,nil))),cons(x,nil)),cons(w,cons(x,cons(u,cons(v,nil)))))
| equal(cons(x,cons(u,cons(v,cons(w,nil)))),cons(w,cons(x,cons(u,cons(v,nil))))) ),
inference(spl,[status(thm),theory(equality)],[35,183]),
[iquote('0:SpL:35.0,183.1')] ).
cnf(6811,plain,
( ~ x2__dfg(s(s(z__dfg)),s(s(s(s(z__dfg)))))
| ~ equal(cons(u,cons(v,cons(w,cons(x,nil)))),cons(w,cons(x,cons(u,cons(v,nil)))))
| equal(cons(x,cons(u,cons(v,cons(w,nil)))),cons(w,cons(x,cons(u,cons(v,nil))))) ),
inference(rew,[status(thm),theory(equality)],[7,6808,16]),
[iquote('0:Rew:7.0,6808.1,16.0,6808.1,16.0,6808.1,16.0,6808.1')] ).
cnf(7204,plain,
( ~ x2__dfg(s(s(z__dfg)),s(s(s(s(z__dfg)))))
| equal(cons(u,cons(v,cons(u,cons(v,nil)))),cons(v,cons(u,cons(v,cons(u,nil))))) ),
inference(eqr,[status(thm),theory(equality)],[6811]),
[iquote('0:EqR:6811.1')] ).
cnf(7349,plain,
( ~ x2__dfg(s(s(z__dfg)),s(s(s(s(z__dfg)))))
| equal(head(cons(u,cons(v,cons(u,cons(v,nil))))),v) ),
inference(spr,[status(thm),theory(equality)],[7204,9]),
[iquote('0:SpR:7204.1,9.0')] ).
cnf(7601,plain,
( ~ x2__dfg(s(s(z__dfg)),s(s(s(s(z__dfg)))))
| equal(u,v) ),
inference(rew,[status(thm),theory(equality)],[9,7349]),
[iquote('0:Rew:9.0,7349.1')] ).
cnf(7604,plain,
( ~ x2__dfg(s(z__dfg),s(s(s(z__dfg))))
| equal(u,v) ),
inference(res,[status(thm),theory(equality)],[15,7601]),
[iquote('0:Res:15.1,7601.0')] ).
cnf(7605,plain,
~ x2__dfg(s(z__dfg),s(s(s(z__dfg)))),
inference(aed,[status(thm),theory(equality)],[5,7604]),
[iquote('0:AED:5.0,7604.1')] ).
cnf(7606,plain,
~ x2__dfg(z__dfg,s(s(z__dfg))),
inference(res,[status(thm),theory(equality)],[15,7605]),
[iquote('0:Res:15.1,7605.0')] ).
cnf(7607,plain,
$false,
inference(mrr,[status(thm)],[7606,2]),
[iquote('0:MRR:7606.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 09:40:21 EDT 2026
% 0.17/0.34 % CPUTime :
% 14.44/14.60
% 14.44/14.60 SPASS V 3.9
% 14.44/14.60 SPASS beiseite: Proof found.
% 14.44/14.60 % SZS status Theorem
% 14.44/14.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.44/14.60 SPASS derived 4531 clauses, backtracked 334 clauses, performed 5 splits and kept 1173 clauses.
% 14.44/14.60 SPASS allocated 107071 KBytes.
% 14.44/14.60 SPASS spent 0:0:14.10 on the problem.
% 14.44/14.60 0:00:00.04 for the input.
% 14.44/14.60 0:00:00.03 for the FLOTTER CNF translation.
% 14.44/14.60 0:00:00.19 for inferences.
% 14.44/14.60 0:00:00.15 for the backtracking.
% 14.44/14.60 0:0:13.65 for the reduction.
% 14.44/14.60
% 14.44/14.60
% 14.44/14.60 Here is a proof with depth 10, length 29 :
% 14.44/14.60 % SZS output start Refutation
% See solution above
% 14.44/14.60 Formulae used in the proof : axiom_006 axiom_010 axiom_005 axiom_012 axiom_016 axiom_001 axiom_007 axiom_008 axiom_013 axiom_015 goal_017
% 14.44/14.60
%------------------------------------------------------------------------------