%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX221+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 0.64s 0.83s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 7 unt; 4 nHn; 39 RR)
% Number of literals : 122 ( 0 equ; 89 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
nf(var(u)),
file('SWX221+1.p',unknown),
[] ).
cnf(20,axiom,
~ equal(lam(u),var(v)),
file('SWX221+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ nf(u)
| nf(lam(u)) ),
file('SWX221+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(app(u,v,w),lam(x)),
file('SWX221+1.p',unknown),
[] ).
cnf(29,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX221+1.p',unknown),
[] ).
cnf(30,axiom,
equal(index(cons(u,v),suc(w)),index(v,w)),
file('SWX221+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX221+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ nf(u)
| ~ nf(v)
| nf(app(u,v,w))
| equal(lam(proj1Lam(u)),u) ),
file('SWX221+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX221+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ nf(u)
| ~ tc(nil,u,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))) ),
file('SWX221+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ tc(u,v,w)
| ~ tc(u,x,arr(w,y))
| tc(u,app(x,v,w),y) ),
file('SWX221+1.p',unknown),
[] ).
cnf(69,plain,
( ~ equal(u,v)
| ~ equal(just(w),just(u))
| tc(cons(w,x),var(zero),v) ),
inference(spl,[status(thm),theory(equality)],[29,41]),
[iquote('0:SpL:29.0,41.1')] ).
cnf(70,plain,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(cons(y,w),var(suc(x)),v) ),
inference(spl,[status(thm),theory(equality)],[30,41]),
[iquote('0:SpL:30.0,41.1')] ).
cnf(74,plain,
( ~ equal(u,v)
| tc(cons(u,w),var(zero),v) ),
inference(eqr,[status(thm),theory(equality)],[69]),
[iquote('0:EqR:69.1')] ).
cnf(78,plain,
( ~ nf(lam(u))
| ~ tc(cons(arr(a,arr(b,c)),nil),u,arr(b,arr(a,c))) ),
inference(res,[status(thm),theory(equality)],[38,42]),
[iquote('0:Res:38.1,42.1')] ).
cnf(81,plain,
( ~ nf(u)
| ~ tc(cons(arr(a,arr(b,c)),nil),u,arr(b,arr(a,c))) ),
inference(sor,[status(thm)],[78,22]),
[iquote('0:SoR:78.0,22.1')] ).
cnf(82,plain,
( ~ nf(lam(u))
| ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),u,arr(a,c)) ),
inference(res,[status(thm),theory(equality)],[38,81]),
[iquote('0:Res:38.1,81.1')] ).
cnf(89,plain,
( ~ nf(u)
| ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),u,arr(a,c)) ),
inference(sor,[status(thm)],[82,22]),
[iquote('0:SoR:82.0,22.1')] ).
cnf(91,plain,
( ~ nf(lam(u))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,c) ),
inference(res,[status(thm),theory(equality)],[38,89]),
[iquote('0:Res:38.1,89.1')] ).
cnf(93,plain,
( ~ nf(u)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,c) ),
inference(sor,[status(thm)],[91,22]),
[iquote('0:SoR:91.0,22.1')] ).
cnf(95,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)],[29,70]),
[iquote('0:SpL:29.0,70.1')] ).
cnf(96,plain,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(cons(y,cons(z,w)),var(suc(suc(x))),v) ),
inference(spl,[status(thm),theory(equality)],[30,70]),
[iquote('0:SpL:30.0,70.1')] ).
cnf(97,plain,
( ~ nf(app(u,v,w))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,arr(w,c)) ),
inference(res,[status(thm),theory(equality)],[43,93]),
[iquote('0:Res:43.2,93.1')] ).
cnf(99,plain,
( ~ equal(u,v)
| tc(cons(w,cons(u,x)),var(suc(zero)),v) ),
inference(eqr,[status(thm),theory(equality)],[95]),
[iquote('0:EqR:95.1')] ).
cnf(110,plain,
( ~ equal(u,v)
| ~ equal(just(w),just(u))
| tc(cons(x,cons(y,cons(w,z))),var(suc(suc(zero))),v) ),
inference(spl,[status(thm),theory(equality)],[29,96]),
[iquote('0:SpL:29.0,96.1')] ).
cnf(112,plain,
( ~ equal(u,v)
| tc(cons(w,cons(x,cons(u,y))),var(suc(suc(zero))),v) ),
inference(eqr,[status(thm),theory(equality)],[110]),
[iquote('0:EqR:110.1')] ).
cnf(195,plain,
( ~ nf(u)
| ~ nf(v)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,arr(w,c))
| equal(lam(proj1Lam(v)),v) ),
inference(sor,[status(thm)],[97,39]),
[iquote('0:SoR:97.0,39.2')] ).
cnf(280,plain,
( ~ nf(u)
| ~ nf(app(v,w,x))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,x)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,arr(x,arr(y,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,y)
| equal(lam(proj1Lam(app(v,w,x))),app(v,w,x)) ),
inference(res,[status(thm),theory(equality)],[43,195]),
[iquote('0:Res:43.2,195.3')] ).
cnf(398,plain,
( ~ nf(u)
| ~ nf(v)
| ~ nf(w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,x)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,arr(x,arr(y,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,y)
| equal(lam(proj1Lam(app(w,v,x))),app(w,v,x))
| equal(lam(proj1Lam(w)),w) ),
inference(sor,[status(thm)],[280,39]),
[iquote('0:SoR:280.1,39.2')] ).
cnf(476,plain,
( ~ nf(u)
| ~ nf(v)
| ~ nf(var(suc(suc(zero))))
| ~ equal(arr(a,arr(b,c)),arr(w,arr(x,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,x)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),v,w))),app(var(suc(suc(zero))),v,w))
| equal(lam(proj1Lam(var(suc(suc(zero))))),var(suc(suc(zero)))) ),
inference(res,[status(thm),theory(equality)],[112,398]),
[iquote('0:Res:112.1,398.4')] ).
cnf(478,plain,
( ~ nf(u)
| ~ nf(v)
| ~ equal(arr(a,arr(b,c)),arr(w,arr(x,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,x)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),v,w))),app(var(suc(suc(zero))),v,w))
| equal(lam(proj1Lam(var(suc(suc(zero))))),var(suc(suc(zero)))) ),
inference(ssi,[status(thm)],[476,1]),
[iquote('0:SSi:476.2,1.0')] ).
cnf(479,plain,
( ~ nf(u)
| ~ nf(v)
| ~ equal(arr(a,arr(b,c)),arr(w,arr(x,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),v,w)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,x)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),v,w))),app(var(suc(suc(zero))),v,w)) ),
inference(mrr,[status(thm)],[478,20]),
[iquote('0:MRR:478.6,20.0')] ).
cnf(602,plain,
( ~ nf(u)
| ~ nf(var(zero))
| ~ equal(a,v)
| ~ equal(arr(a,arr(b,c)),arr(v,arr(w,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,w)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),v))),app(var(suc(suc(zero))),var(zero),v)) ),
inference(res,[status(thm),theory(equality)],[74,479]),
[iquote('0:Res:74.1,479.3')] ).
cnf(605,plain,
( ~ nf(u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(b,c)),arr(v,arr(w,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,w)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),v))),app(var(suc(suc(zero))),var(zero),v)) ),
inference(ssi,[status(thm)],[602,1]),
[iquote('0:SSi:602.1,1.0')] ).
cnf(686,plain,
( ~ nf(var(suc(zero)))
| ~ equal(b,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(b,c)),arr(v,arr(u,c)))
| equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),v))),app(var(suc(suc(zero))),var(zero),v)) ),
inference(res,[status(thm),theory(equality)],[99,605]),
[iquote('0:Res:99.1,605.3')] ).
cnf(689,plain,
( ~ equal(b,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(b,c)),arr(v,arr(u,c)))
| equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),v))),app(var(suc(suc(zero))),var(zero),v)) ),
inference(ssi,[status(thm)],[686,1]),
[iquote('0:SSi:686.0,1.0')] ).
cnf(693,plain,
( ~ equal(b,b)
| ~ equal(a,a)
| equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))),app(var(suc(suc(zero))),var(zero),a)) ),
inference(eqr,[status(thm),theory(equality)],[689]),
[iquote('0:EqR:689.2')] ).
cnf(694,plain,
equal(lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))),app(var(suc(suc(zero))),var(zero),a)),
inference(obv,[status(thm),theory(equality)],[693]),
[iquote('0:Obv:693.1')] ).
cnf(695,plain,
$false,
inference(unc,[status(thm)],[694,27]),
[iquote('0:UnC:694.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX221+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 12:29:19 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.64/0.83
% 0.64/0.83 SPASS V 3.9
% 0.64/0.83 SPASS beiseite: Proof found.
% 0.64/0.83 % SZS status Theorem
% 0.64/0.83 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.83 SPASS derived 430 clauses, backtracked 0 clauses, performed 0 splits and kept 376 clauses.
% 0.64/0.83 SPASS allocated 99207 KBytes.
% 0.64/0.83 SPASS spent 0:00:00.47 on the problem.
% 0.64/0.83 0:00:00.03 for the input.
% 0.64/0.83 0:00:00.03 for the FLOTTER CNF translation.
% 0.64/0.83 0:00:00.10 for inferences.
% 0.64/0.83 0:00:00.00 for the backtracking.
% 0.64/0.83 0:00:00.26 for the reduction.
% 0.64/0.83
% 0.64/0.83
% 0.64/0.83 Here is a proof with depth 14, length 39 :
% 0.64/0.83 % SZS output start Refutation
% See solution above
% 0.64/0.83 Formulae used in the proof : axiom_027 axiom_023 axiom_026 axiom_021 axiom_029 axiom_030 axiom_033 axiom_024 axiom_035 goal_036 axiom_031
% 0.64/0.83
%------------------------------------------------------------------------------