%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX223+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 07:07:27 PM UTC 2026
% Result : Theorem 0.47s 0.64s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 7 unt; 4 nHn; 34 RR)
% Number of literals : 110 ( 0 equ; 80 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
nf(var(u)),
file('SWX223+1.p',unknown),
[] ).
cnf(20,axiom,
~ equal(lam(u),var(v)),
file('SWX223+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ nf(u)
| nf(lam(u)) ),
file('SWX223+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(app(u,v,w),lam(x)),
file('SWX223+1.p',unknown),
[] ).
cnf(29,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX223+1.p',unknown),
[] ).
cnf(30,axiom,
equal(index(cons(u,v),suc(w)),index(v,w)),
file('SWX223+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX223+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ nf(u)
| ~ tc(nil,u,arr(arr(a,arr(a,b)),arr(a,b))) ),
file('SWX223+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ nf(u)
| ~ nf(v)
| nf(app(u,v,w))
| equal(lam(proj1Lam(u)),u) ),
file('SWX223+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX223+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ tc(u,v,w)
| ~ tc(u,x,arr(w,y))
| tc(u,app(x,v,w),y) ),
file('SWX223+1.p',unknown),
[] ).
cnf(63,plain,
( ~ nf(lam(u))
| ~ tc(cons(arr(a,arr(a,b)),nil),u,arr(a,b)) ),
inference(res,[status(thm),theory(equality)],[38,39]),
[iquote('0:Res:38.1,39.1')] ).
cnf(70,plain,
( ~ equal(u,v)
| ~ equal(just(w),just(u))
| tc(cons(w,x),var(zero),v) ),
inference(spl,[status(thm),theory(equality)],[29,42]),
[iquote('0:SpL:29.0,42.1')] ).
cnf(71,plain,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(cons(y,w),var(suc(x)),v) ),
inference(spl,[status(thm),theory(equality)],[30,42]),
[iquote('0:SpL:30.0,42.1')] ).
cnf(75,plain,
( ~ nf(u)
| ~ tc(cons(arr(a,arr(a,b)),nil),u,arr(a,b)) ),
inference(sor,[status(thm)],[63,22]),
[iquote('0:SoR:63.0,22.1')] ).
cnf(80,plain,
( ~ nf(lam(u))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,b) ),
inference(res,[status(thm),theory(equality)],[38,75]),
[iquote('0:Res:38.1,75.1')] ).
cnf(81,plain,
( ~ nf(u)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,b) ),
inference(sor,[status(thm)],[80,22]),
[iquote('0:SoR:80.0,22.1')] ).
cnf(82,plain,
( ~ nf(app(u,v,w))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,arr(w,b)) ),
inference(res,[status(thm),theory(equality)],[43,81]),
[iquote('0:Res:43.2,81.1')] ).
cnf(83,plain,
( ~ equal(u,v)
| tc(cons(u,w),var(zero),v) ),
inference(eqr,[status(thm),theory(equality)],[70]),
[iquote('0:EqR:70.1')] ).
cnf(93,plain,
( ~ equal(u,v)
| ~ equal(just(w),just(u))
| tc(cons(x,cons(w,y)),var(suc(zero)),v) ),
inference(spl,[status(thm),theory(equality)],[29,71]),
[iquote('0:SpL:29.0,71.1')] ).
cnf(95,plain,
( ~ equal(u,v)
| tc(cons(w,cons(u,x)),var(suc(zero)),v) ),
inference(eqr,[status(thm),theory(equality)],[93]),
[iquote('0:EqR:93.1')] ).
cnf(143,plain,
( ~ nf(u)
| ~ nf(v)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,arr(w,b))
| equal(lam(proj1Lam(v)),v) ),
inference(sor,[status(thm)],[82,40]),
[iquote('0:SoR:82.0,40.2')] ).
cnf(190,plain,
( ~ nf(u)
| ~ nf(app(v,w,x))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,x)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,arr(x,arr(y,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,y)
| equal(lam(proj1Lam(app(v,w,x))),app(v,w,x)) ),
inference(res,[status(thm),theory(equality)],[43,143]),
[iquote('0:Res:43.2,143.3')] ).
cnf(258,plain,
( ~ nf(u)
| ~ nf(v)
| ~ nf(w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,x)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,arr(x,arr(y,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,y)
| equal(lam(proj1Lam(app(w,v,x))),app(w,v,x))
| equal(lam(proj1Lam(w)),w) ),
inference(sor,[status(thm)],[190,40]),
[iquote('0:SoR:190.1,40.2')] ).
cnf(313,plain,
( ~ nf(u)
| ~ nf(v)
| ~ nf(var(suc(zero)))
| ~ equal(arr(a,arr(a,b)),arr(w,arr(x,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,x)
| equal(lam(proj1Lam(app(var(suc(zero)),v,w))),app(var(suc(zero)),v,w))
| equal(lam(proj1Lam(var(suc(zero)))),var(suc(zero))) ),
inference(res,[status(thm),theory(equality)],[95,258]),
[iquote('0:Res:95.1,258.4')] ).
cnf(314,plain,
( ~ nf(u)
| ~ nf(v)
| ~ equal(arr(a,arr(a,b)),arr(w,arr(x,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,x)
| equal(lam(proj1Lam(app(var(suc(zero)),v,w))),app(var(suc(zero)),v,w))
| equal(lam(proj1Lam(var(suc(zero)))),var(suc(zero))) ),
inference(ssi,[status(thm)],[313,1]),
[iquote('0:SSi:313.2,1.0')] ).
cnf(315,plain,
( ~ nf(u)
| ~ nf(v)
| ~ equal(arr(a,arr(a,b)),arr(w,arr(x,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),v,w)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,x)
| equal(lam(proj1Lam(app(var(suc(zero)),v,w))),app(var(suc(zero)),v,w)) ),
inference(mrr,[status(thm)],[314,20]),
[iquote('0:MRR:314.6,20.0')] ).
cnf(403,plain,
( ~ nf(u)
| ~ nf(var(zero))
| ~ equal(a,v)
| ~ equal(arr(a,arr(a,b)),arr(v,arr(w,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,w)
| equal(lam(proj1Lam(app(var(suc(zero)),var(zero),v))),app(var(suc(zero)),var(zero),v)) ),
inference(res,[status(thm),theory(equality)],[83,315]),
[iquote('0:Res:83.1,315.3')] ).
cnf(405,plain,
( ~ nf(u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(a,b)),arr(v,arr(w,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,w)
| equal(lam(proj1Lam(app(var(suc(zero)),var(zero),v))),app(var(suc(zero)),var(zero),v)) ),
inference(ssi,[status(thm)],[403,1]),
[iquote('0:SSi:403.1,1.0')] ).
cnf(489,plain,
( ~ nf(var(zero))
| ~ equal(a,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(a,b)),arr(v,arr(u,b)))
| equal(lam(proj1Lam(app(var(suc(zero)),var(zero),v))),app(var(suc(zero)),var(zero),v)) ),
inference(res,[status(thm),theory(equality)],[83,405]),
[iquote('0:Res:83.1,405.3')] ).
cnf(491,plain,
( ~ equal(a,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(a,b)),arr(v,arr(u,b)))
| equal(lam(proj1Lam(app(var(suc(zero)),var(zero),v))),app(var(suc(zero)),var(zero),v)) ),
inference(ssi,[status(thm)],[489,1]),
[iquote('0:SSi:489.0,1.0')] ).
cnf(494,plain,
( ~ equal(a,a)
| ~ equal(a,a)
| equal(lam(proj1Lam(app(var(suc(zero)),var(zero),a))),app(var(suc(zero)),var(zero),a)) ),
inference(eqr,[status(thm),theory(equality)],[491]),
[iquote('0:EqR:491.2')] ).
cnf(495,plain,
equal(lam(proj1Lam(app(var(suc(zero)),var(zero),a))),app(var(suc(zero)),var(zero),a)),
inference(obv,[status(thm),theory(equality)],[494]),
[iquote('0:Obv:494.1')] ).
cnf(496,plain,
$false,
inference(unc,[status(thm)],[495,27]),
[iquote('0:UnC:495.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX223+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.17/0.34 % Computer : n019.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 12:36:14 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.47/0.64
% 0.47/0.64 SPASS V 3.9
% 0.47/0.64 SPASS beiseite: Proof found.
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.64 SPASS derived 306 clauses, backtracked 0 clauses, performed 0 splits and kept 273 clauses.
% 0.47/0.64 SPASS allocated 98699 KBytes.
% 0.47/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.47/0.64 0:00:00.03 for the input.
% 0.47/0.64 0:00:00.03 for the FLOTTER CNF translation.
% 0.47/0.64 0:00:00.04 for inferences.
% 0.47/0.64 0:00:00.00 for the backtracking.
% 0.47/0.64 0:00:00.14 for the reduction.
% 0.47/0.64
% 0.47/0.64
% 0.47/0.64 Here is a proof with depth 12, length 34 :
% 0.47/0.64 % SZS output start Refutation
% See solution above
% 0.47/0.64 Formulae used in the proof : axiom_027 axiom_023 axiom_026 axiom_021 axiom_029 axiom_030 axiom_033 goal_036 axiom_024 axiom_035 axiom_031
% 0.47/0.64
%------------------------------------------------------------------------------