%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX220+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 2.43s 2.60s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 7 unt; 0 nHn; 24 RR)
% Number of literals : 52 ( 0 equ; 38 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(25,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX220+1.p',unknown),
[] ).
cnf(26,axiom,
equal(index(cons(u,v),suc(w)),index(v,w)),
file('SWX220+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX220+1.p',unknown),
[] ).
cnf(33,axiom,
~ tc(nil,u,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
file('SWX220+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX220+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ tc(u,v,w)
| ~ tc(u,x,arr(w,y))
| tc(u,app(x,v,w),y) ),
file('SWX220+1.p',unknown),
[] ).
cnf(40,plain,
~ tc(cons(arr(a,arr(b,c)),nil),u,arr(b,arr(a,c))),
inference(res,[status(thm),theory(equality)],[32,33]),
[iquote('0:Res:32.1,33.0')] ).
cnf(61,plain,
~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),u,arr(a,c)),
inference(res,[status(thm),theory(equality)],[32,40]),
[iquote('0:Res:32.1,40.0')] ).
cnf(63,plain,
( ~ equal(u,v)
| ~ equal(just(w),just(u))
| tc(cons(w,x),var(zero),v) ),
inference(spl,[status(thm),theory(equality)],[25,35]),
[iquote('0:SpL:25.0,35.1')] ).
cnf(64,plain,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(cons(y,w),var(suc(x)),v) ),
inference(spl,[status(thm),theory(equality)],[26,35]),
[iquote('0:SpL:26.0,35.1')] ).
cnf(65,plain,
~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,c),
inference(res,[status(thm),theory(equality)],[32,61]),
[iquote('0:Res:32.1,61.0')] ).
cnf(71,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,v)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,arr(v,c)) ),
inference(res,[status(thm),theory(equality)],[36,65]),
[iquote('0:Res:36.2,65.0')] ).
cnf(76,plain,
( ~ equal(u,v)
| tc(cons(u,w),var(zero),v) ),
inference(eqr,[status(thm),theory(equality)],[63]),
[iquote('0:EqR:63.1')] ).
cnf(85,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)],[25,64]),
[iquote('0:SpL:25.0,64.1')] ).
cnf(86,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)],[26,64]),
[iquote('0:SpL:26.0,64.1')] ).
cnf(88,plain,
( ~ equal(u,v)
| tc(cons(w,cons(u,x)),var(suc(zero)),v) ),
inference(eqr,[status(thm),theory(equality)],[85]),
[iquote('0:EqR:85.1')] ).
cnf(107,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)],[25,86]),
[iquote('0:SpL:25.0,86.1')] ).
cnf(144,plain,
( ~ equal(u,v)
| tc(cons(w,cons(x,cons(u,y))),var(suc(suc(zero))),v) ),
inference(eqr,[status(thm),theory(equality)],[107]),
[iquote('0:EqR:107.1')] ).
cnf(423,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),u,v)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,arr(v,arr(x,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),y,x) ),
inference(res,[status(thm),theory(equality)],[36,71]),
[iquote('0:Res:36.2,71.1')] ).
cnf(1120,plain,
( ~ equal(arr(a,arr(b,c)),arr(u,arr(v,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,u)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),x,v) ),
inference(res,[status(thm),theory(equality)],[144,423]),
[iquote('0:Res:144.1,423.1')] ).
cnf(1903,plain,
( ~ equal(a,u)
| ~ equal(arr(a,arr(b,c)),arr(u,arr(v,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),w,v) ),
inference(res,[status(thm),theory(equality)],[76,1120]),
[iquote('0:Res:76.1,1120.1')] ).
cnf(3044,plain,
( ~ equal(b,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(b,c)),arr(v,arr(u,c))) ),
inference(res,[status(thm),theory(equality)],[88,1903]),
[iquote('0:Res:88.1,1903.2')] ).
cnf(3047,plain,
( ~ equal(b,b)
| ~ equal(a,a) ),
inference(eqr,[status(thm),theory(equality)],[3044]),
[iquote('0:EqR:3044.2')] ).
cnf(3048,plain,
$false,
inference(obv,[status(thm),theory(equality)],[3047]),
[iquote('0:Obv:3047.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX220+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 12:25:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 2.43/2.60
% 2.43/2.60 SPASS V 3.9
% 2.43/2.60 SPASS beiseite: Proof found.
% 2.43/2.60 % SZS status Theorem
% 2.43/2.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.43/2.60 SPASS derived 2779 clauses, backtracked 0 clauses, performed 0 splits and kept 1899 clauses.
% 2.43/2.60 SPASS allocated 88239 KBytes.
% 2.43/2.60 SPASS spent 0:00:02.25 on the problem.
% 2.43/2.60 0:00:00.04 for the input.
% 2.43/2.60 0:00:00.03 for the FLOTTER CNF translation.
% 2.43/2.60 0:00:00.62 for inferences.
% 2.43/2.60 0:00:00.00 for the backtracking.
% 2.43/2.60 0:00:01.50 for the reduction.
% 2.43/2.60
% 2.43/2.60
% 2.43/2.60 Here is a proof with depth 9, length 24 :
% 2.43/2.60 % SZS output start Refutation
% See solution above
% 2.43/2.60 Formulae used in the proof : axiom_025 axiom_026 axiom_029 goal_032 axiom_031 axiom_027
% 2.43/2.60
%------------------------------------------------------------------------------