%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 07:07:23 PM UTC 2026
% Result : Theorem 0.72s 0.90s
% Output : Refutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of clauses : 67 ( 19 unt; 27 nHn; 67 RR)
% Number of literals : 143 ( 0 equ; 47 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
leqNat(z__dfg,u),
file('SWX199+1.p',unknown),
[] ).
cnf(4,axiom,
~ leqNat(s(u),z__dfg),
file('SWX199+1.p',unknown),
[] ).
cnf(5,axiom,
equal(merge(nil,u),u),
file('SWX199+1.p',unknown),
[] ).
cnf(6,axiom,
equal(head(cons(u,v)),u),
file('SWX199+1.p',unknown),
[] ).
cnf(7,axiom,
equal(tail(cons(u,v)),v),
file('SWX199+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(cons(u,v),nil),
file('SWX199+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ leqNat(s(u),s(v))
| leqNat(u,v) ),
file('SWX199+1.p',unknown),
[] ).
cnf(11,axiom,
equal(merge(cons(u,v),nil),cons(u,v)),
file('SWX199+1.p',unknown),
[] ).
cnf(12,axiom,
( leqNat(u,v)
| equal(merge(cons(u,w),cons(v,x)),cons(v,merge(cons(u,w),x))) ),
file('SWX199+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ leqNat(u,v)
| equal(merge(cons(u,w),cons(v,x)),cons(u,merge(w,cons(v,x)))) ),
file('SWX199+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ equal(merge(u,v),merge(v,u))
| ~ equal(merge(u,w),merge(w,u))
| equal(merge(w,v),merge(v,w)) ),
file('SWX199+1.p',unknown),
[] ).
cnf(25,plain,
( ~ equal(merge(u,nil),u)
| ~ equal(merge(nil,v),merge(v,nil))
| equal(merge(v,u),merge(u,v)) ),
inference(spl,[status(thm),theory(equality)],[5,14]),
[iquote('0:SpL:5.0,14.0')] ).
cnf(26,plain,
( ~ equal(merge(nil,cons(u,v)),cons(u,v))
| ~ equal(merge(cons(u,v),w),merge(w,cons(u,v)))
| equal(merge(w,nil),merge(nil,w)) ),
inference(spl,[status(thm),theory(equality)],[11,14]),
[iquote('0:SpL:11.0,14.0')] ).
cnf(30,plain,
( ~ equal(merge(nil,cons(u,v)),cons(u,v))
| ~ equal(merge(nil,w),merge(w,nil))
| equal(merge(w,cons(u,v)),merge(cons(u,v),w)) ),
inference(spl,[status(thm),theory(equality)],[11,14]),
[iquote('0:SpL:11.0,14.0')] ).
cnf(34,plain,
( ~ equal(merge(u,nil),u)
| ~ equal(merge(v,nil),v)
| equal(merge(v,u),merge(u,v)) ),
inference(rew,[status(thm),theory(equality)],[5,25]),
[iquote('0:Rew:5.0,25.1')] ).
cnf(35,plain,
( ~ equal(cons(u,v),cons(u,v))
| ~ equal(merge(w,nil),w)
| equal(merge(w,cons(u,v)),merge(cons(u,v),w)) ),
inference(rew,[status(thm),theory(equality)],[5,30]),
[iquote('0:Rew:5.0,30.1,5.0,30.0')] ).
cnf(36,plain,
( ~ equal(merge(u,nil),u)
| equal(merge(u,cons(v,w)),merge(cons(v,w),u)) ),
inference(obv,[status(thm),theory(equality)],[35]),
[iquote('0:Obv:35.0')] ).
cnf(37,plain,
( ~ equal(cons(u,v),cons(u,v))
| ~ equal(merge(cons(u,v),w),merge(w,cons(u,v)))
| equal(merge(w,nil),w) ),
inference(rew,[status(thm),theory(equality)],[5,26]),
[iquote('0:Rew:5.0,26.2,5.0,26.0')] ).
cnf(38,plain,
( ~ equal(merge(cons(u,v),w),merge(w,cons(u,v)))
| equal(merge(w,nil),w) ),
inference(obv,[status(thm),theory(equality)],[37]),
[iquote('0:Obv:37.0')] ).
cnf(62,plain,
( ~ equal(merge(cons(u,v),nil),cons(u,v))
| leqNat(w,u)
| equal(merge(cons(u,v),cons(w,x)),cons(u,merge(cons(w,x),v))) ),
inference(spr,[status(thm),theory(equality)],[36,12]),
[iquote('0:SpR:36.1,12.1')] ).
cnf(63,plain,
( ~ equal(merge(cons(u,v),nil),cons(u,v))
| ~ leqNat(w,u)
| equal(merge(cons(u,v),cons(w,x)),cons(w,merge(x,cons(u,v)))) ),
inference(spr,[status(thm),theory(equality)],[36,13]),
[iquote('0:SpR:36.1,13.1')] ).
cnf(73,plain,
( ~ equal(cons(u,v),cons(u,v))
| leqNat(w,u)
| equal(merge(cons(u,v),cons(w,x)),cons(u,merge(cons(w,x),v))) ),
inference(rew,[status(thm),theory(equality)],[11,62]),
[iquote('0:Rew:11.0,62.0')] ).
cnf(74,plain,
( leqNat(u,v)
| equal(merge(cons(v,w),cons(u,x)),cons(v,merge(cons(u,x),w))) ),
inference(obv,[status(thm),theory(equality)],[73]),
[iquote('0:Obv:73.0')] ).
cnf(81,plain,
( ~ equal(cons(u,v),cons(u,v))
| ~ leqNat(w,u)
| equal(merge(cons(u,v),cons(w,x)),cons(w,merge(x,cons(u,v)))) ),
inference(rew,[status(thm),theory(equality)],[11,63]),
[iquote('0:Rew:11.0,63.0')] ).
cnf(82,plain,
( ~ leqNat(u,v)
| equal(merge(cons(v,w),cons(u,x)),cons(u,merge(x,cons(v,w)))) ),
inference(obv,[status(thm),theory(equality)],[81]),
[iquote('0:Obv:81.0')] ).
cnf(107,plain,
( leqNat(u,v)
| leqNat(v,u)
| equal(cons(v,merge(cons(u,w),x)),cons(u,merge(cons(v,x),w))) ),
inference(spr,[status(thm),theory(equality)],[74,12]),
[iquote('0:SpR:74.1,12.1')] ).
cnf(108,plain,
( ~ leqNat(u,v)
| leqNat(v,u)
| equal(cons(u,merge(cons(v,w),x)),cons(u,merge(x,cons(v,w)))) ),
inference(spr,[status(thm),theory(equality)],[74,13]),
[iquote('0:SpR:74.1,13.1')] ).
cnf(145,plain,
( ~ leqNat(u,v)
| ~ leqNat(v,u)
| equal(cons(u,merge(w,cons(v,x))),cons(v,merge(x,cons(u,w)))) ),
inference(spr,[status(thm),theory(equality)],[82,13]),
[iquote('0:SpR:82.1,13.1')] ).
cnf(175,plain,
( leqNat(u,v)
| leqNat(v,u)
| equal(tail(cons(v,merge(cons(u,w),x))),merge(cons(v,x),w)) ),
inference(spr,[status(thm),theory(equality)],[107,7]),
[iquote('0:SpR:107.2,7.0')] ).
cnf(211,plain,
( leqNat(u,v)
| leqNat(v,u)
| equal(merge(cons(u,w),x),merge(cons(v,x),w)) ),
inference(rew,[status(thm),theory(equality)],[7,175]),
[iquote('0:Rew:7.0,175.2')] ).
cnf(609,plain,
( ~ leqNat(u,v)
| leqNat(v,u)
| equal(tail(cons(u,merge(cons(v,w),x))),merge(x,cons(v,w))) ),
inference(spr,[status(thm),theory(equality)],[108,7]),
[iquote('0:SpR:108.2,7.0')] ).
cnf(660,plain,
( ~ leqNat(u,v)
| leqNat(v,u)
| equal(merge(cons(v,w),x),merge(x,cons(v,w))) ),
inference(rew,[status(thm),theory(equality)],[7,609]),
[iquote('0:Rew:7.0,609.2')] ).
cnf(831,plain,
( ~ leqNat(u,v)
| ~ leqNat(v,u)
| equal(tail(cons(u,merge(w,cons(v,x)))),merge(x,cons(u,w))) ),
inference(spr,[status(thm),theory(equality)],[145,7]),
[iquote('0:SpR:145.2,7.0')] ).
cnf(892,plain,
( ~ leqNat(u,v)
| ~ leqNat(v,u)
| equal(merge(w,cons(v,x)),merge(x,cons(u,w))) ),
inference(rew,[status(thm),theory(equality)],[7,831]),
[iquote('0:Rew:7.0,831.2')] ).
cnf(973,plain,
( leqNat(u,u)
| equal(merge(cons(u,v),w),merge(cons(u,w),v)) ),
inference(fac,[status(thm)],[211]),
[iquote('0:Fac:211.0,211.1')] ).
cnf(1092,plain,
( leqNat(u,u)
| equal(merge(cons(u,nil),v),cons(u,v)) ),
inference(spr,[status(thm),theory(equality)],[973,11]),
[iquote('0:SpR:973.1,11.0')] ).
cnf(1110,plain,
( ~ equal(merge(u,nil),u)
| leqNat(v,v)
| equal(merge(cons(v,u),w),merge(u,cons(v,w))) ),
inference(spr,[status(thm),theory(equality)],[973,36]),
[iquote('0:SpR:973.1,36.1')] ).
cnf(1224,plain,
( equal(merge(cons(s(u),nil),v),cons(s(u),v))
| leqNat(u,u) ),
inference(res,[status(thm),theory(equality)],[1092,9]),
[iquote('0:Res:1092.0,9.0')] ).
cnf(1273,plain,
( ~ equal(merge(u,cons(s(v),nil)),cons(s(v),u))
| leqNat(v,v)
| equal(merge(u,nil),u) ),
inference(spl,[status(thm),theory(equality)],[1224,38]),
[iquote('0:SpL:1224.0,38.0')] ).
cnf(1299,plain,
( leqNat(u,z__dfg)
| equal(merge(cons(u,v),w),merge(w,cons(u,v))) ),
inference(res,[status(thm),theory(equality)],[1,660]),
[iquote('0:Res:1.0,660.0')] ).
cnf(1371,plain,
( leqNat(s(u),z__dfg)
| equal(merge(v,cons(s(u),nil)),cons(s(u),v))
| leqNat(u,u) ),
inference(spr,[status(thm),theory(equality)],[1299,1224]),
[iquote('0:SpR:1299.1,1224.0')] ).
cnf(1434,plain,
( ~ equal(merge(cons(u,v),w),merge(cons(u,v),w))
| leqNat(u,z__dfg)
| equal(merge(w,nil),w) ),
inference(spl,[status(thm),theory(equality)],[1299,38]),
[iquote('0:SpL:1299.1,38.0')] ).
cnf(1440,plain,
( equal(merge(u,cons(s(v),nil)),cons(s(v),u))
| leqNat(v,v) ),
inference(mrr,[status(thm)],[1371,4]),
[iquote('0:MRR:1371.0,4.0')] ).
cnf(1445,plain,
( ~ equal(cons(s(u),v),cons(s(u),v))
| leqNat(u,u)
| equal(merge(v,nil),v) ),
inference(rew,[status(thm),theory(equality)],[1440,1273]),
[iquote('0:Rew:1440.0,1273.0')] ).
cnf(1446,plain,
( leqNat(u,u)
| equal(merge(v,nil),v) ),
inference(obv,[status(thm),theory(equality)],[1445]),
[iquote('0:Obv:1445.0')] ).
cnf(1450,plain,
( ~ equal(u,u)
| leqNat(v,v)
| equal(merge(cons(v,u),w),merge(u,cons(v,w))) ),
inference(rew,[status(thm),theory(equality)],[1446,1110]),
[iquote('0:Rew:1446.1,1110.0')] ).
cnf(1455,plain,
( leqNat(u,u)
| equal(merge(cons(u,v),w),merge(v,cons(u,w))) ),
inference(obv,[status(thm),theory(equality)],[1450]),
[iquote('0:Obv:1450.0')] ).
cnf(1457,plain,
( leqNat(u,u)
| equal(merge(cons(u,v),w),merge(w,cons(u,v))) ),
inference(rew,[status(thm),theory(equality)],[1455,973]),
[iquote('0:Rew:1455.1,973.1')] ).
cnf(1468,plain,
( leqNat(u,u)
| equal(merge(v,cons(u,w)),merge(w,cons(u,v))) ),
inference(rew,[status(thm),theory(equality)],[1455,1457]),
[iquote('0:Rew:1455.1,1457.1')] ).
cnf(1469,plain,
( leqNat(u,z__dfg)
| equal(merge(v,nil),v) ),
inference(obv,[status(thm),theory(equality)],[1434]),
[iquote('0:Obv:1434.0')] ).
cnf(1514,plain,
equal(merge(u,nil),u),
inference(spt,[spt(split,[position(s1)])],[1469]),
[iquote('1:Spt:1469.1')] ).
cnf(1515,plain,
( ~ equal(merge(u,nil),u)
| ~ equal(v,v)
| equal(merge(v,u),merge(u,v)) ),
inference(rew,[status(thm),theory(equality)],[1514,34]),
[iquote('1:Rew:1514.0,34.1')] ).
cnf(1524,plain,
( ~ equal(merge(u,nil),u)
| equal(merge(v,u),merge(u,v)) ),
inference(obv,[status(thm),theory(equality)],[1515]),
[iquote('1:Obv:1515.1')] ).
cnf(1525,plain,
( ~ equal(u,u)
| equal(merge(v,u),merge(u,v)) ),
inference(rew,[status(thm),theory(equality)],[1514,1524]),
[iquote('1:Rew:1514.0,1524.0')] ).
cnf(1526,plain,
equal(merge(u,v),merge(v,u)),
inference(obv,[status(thm),theory(equality)],[1525]),
[iquote('1:Obv:1525.0')] ).
cnf(1868,plain,
( ~ leqNat(u,u)
| equal(merge(v,cons(u,w)),merge(w,cons(u,v)))
| equal(merge(x,cons(u,y)),merge(y,cons(u,x))) ),
inference(res,[status(thm),theory(equality)],[1468,892]),
[iquote('0:Res:1468.0,892.0')] ).
cnf(1890,plain,
( ~ leqNat(u,u)
| equal(merge(v,cons(u,w)),merge(w,cons(u,v))) ),
inference(con,[status(thm)],[1868]),
[iquote('0:Con:1868.2')] ).
cnf(1891,plain,
equal(merge(u,cons(v,w)),merge(w,cons(v,u))),
inference(mrr,[status(thm)],[1890,1468]),
[iquote('0:MRR:1890.0,1468.0')] ).
cnf(1901,plain,
equal(merge(u,cons(v,nil)),cons(v,u)),
inference(spr,[status(thm),theory(equality)],[1891,5]),
[iquote('0:SpR:1891.0,5.0')] ).
cnf(1902,plain,
equal(merge(cons(u,v),w),merge(v,cons(u,w))),
inference(spr,[status(thm),theory(equality)],[1891,1526]),
[iquote('1:SpR:1891.0,1526.0')] ).
cnf(2178,plain,
equal(merge(u,cons(v,cons(w,nil))),cons(w,cons(v,u))),
inference(spr,[status(thm),theory(equality)],[1902,1901]),
[iquote('1:SpR:1902.0,1901.0')] ).
cnf(2187,plain,
equal(cons(u,cons(v,nil)),cons(v,cons(u,nil))),
inference(spr,[status(thm),theory(equality)],[2178,5]),
[iquote('1:SpR:2178.0,5.0')] ).
cnf(2279,plain,
equal(head(cons(u,cons(v,nil))),v),
inference(spr,[status(thm),theory(equality)],[2187,6]),
[iquote('1:SpR:2187.0,6.0')] ).
cnf(2294,plain,
equal(u,v),
inference(rew,[status(thm),theory(equality)],[6,2279]),
[iquote('1:Rew:6.0,2279.0')] ).
cnf(2295,plain,
$false,
inference(unc,[status(thm)],[2294,8]),
[iquote('1:UnC:2294.0,8.0')] ).
cnf(2314,plain,
leqNat(u,z__dfg),
inference(spt,[spt(split,[position(s2)])],[1469]),
[iquote('1:Spt:2295.0,1469.0')] ).
cnf(2315,plain,
$false,
inference(unc,[status(thm)],[2314,4]),
[iquote('1:UnC:2314.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : run_spass %d %s
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 11:11:45 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.72/0.90
% 0.72/0.90 SPASS V 3.9
% 0.72/0.90 SPASS beiseite: Proof found.
% 0.72/0.90 % SZS status Theorem
% 0.72/0.90 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.72/0.90 SPASS derived 1812 clauses, backtracked 207 clauses, performed 1 splits and kept 710 clauses.
% 0.72/0.90 SPASS allocated 87521 KBytes.
% 0.72/0.90 SPASS spent 0:00:00.63 on the problem.
% 0.72/0.90 0:00:00.02 for the input.
% 0.72/0.90 0:00:00.02 for the FLOTTER CNF translation.
% 0.72/0.90 0:00:00.03 for inferences.
% 0.72/0.90 0:00:00.00 for the backtracking.
% 0.72/0.90 0:00:00.54 for the reduction.
% 0.72/0.90
% 0.72/0.90
% 0.72/0.90 Here is a proof with depth 10, length 67 :
% 0.72/0.90 % SZS output start Refutation
% See solution above
% 0.72/0.90 Formulae used in the proof : axiom_006 axiom_007 axiom_009 axiom_001 axiom_002 axiom_003 axiom_008 axiom_010 axiom_012 axiom_011 goal_013
% 0.72/0.90
%------------------------------------------------------------------------------