%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX224+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 0.74s 0.94s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 6 unt; 0 nHn; 20 RR)
% Number of literals : 43 ( 0 equ; 32 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(25,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX224+1.p',unknown),
[] ).
cnf(26,axiom,
equal(index(cons(u,v),suc(w)),index(v,w)),
file('SWX224+1.p',unknown),
[] ).
cnf(29,axiom,
~ tc(nil,u,arr(arr(a,arr(a,b)),arr(a,b))),
file('SWX224+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX224+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX224+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ tc(u,v,w)
| ~ tc(u,x,arr(w,y))
| tc(u,app(x,v,w),y) ),
file('SWX224+1.p',unknown),
[] ).
cnf(39,plain,
~ tc(cons(arr(a,arr(a,b)),nil),u,arr(a,b)),
inference(res,[status(thm),theory(equality)],[33,29]),
[iquote('0:Res:33.1,29.0')] ).
cnf(59,plain,
~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,b),
inference(res,[status(thm),theory(equality)],[33,39]),
[iquote('0:Res:33.1,39.0')] ).
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(68,plain,
( ~ equal(u,v)
| tc(cons(u,w),var(zero),v) ),
inference(eqr,[status(thm),theory(equality)],[63]),
[iquote('0:EqR:63.1')] ).
cnf(74,plain,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,v)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,arr(v,b)) ),
inference(res,[status(thm),theory(equality)],[36,59]),
[iquote('0:Res:36.2,59.0')] ).
cnf(83,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(91,plain,
( ~ equal(u,v)
| tc(cons(w,cons(u,x)),var(suc(zero)),v) ),
inference(eqr,[status(thm),theory(equality)],[83]),
[iquote('0:EqR:83.1')] ).
cnf(199,plain,
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),u,v)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,arr(v,arr(x,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),y,x) ),
inference(res,[status(thm),theory(equality)],[36,74]),
[iquote('0:Res:36.2,74.1')] ).
cnf(457,plain,
( ~ equal(arr(a,arr(a,b)),arr(u,arr(v,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,u)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),x,v) ),
inference(res,[status(thm),theory(equality)],[91,199]),
[iquote('0:Res:91.1,199.1')] ).
cnf(730,plain,
( ~ equal(a,u)
| ~ equal(arr(a,arr(a,b)),arr(u,arr(v,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),w,v) ),
inference(res,[status(thm),theory(equality)],[68,457]),
[iquote('0:Res:68.1,457.1')] ).
cnf(1123,plain,
( ~ equal(a,u)
| ~ equal(a,v)
| ~ equal(arr(a,arr(a,b)),arr(v,arr(u,b))) ),
inference(res,[status(thm),theory(equality)],[68,730]),
[iquote('0:Res:68.1,730.2')] ).
cnf(1125,plain,
( ~ equal(a,a)
| ~ equal(a,a) ),
inference(eqr,[status(thm),theory(equality)],[1123]),
[iquote('0:EqR:1123.2')] ).
cnf(1126,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1125]),
[iquote('0:Obv:1125.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX224+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 12:39:44 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.74/0.94
% 0.74/0.94 SPASS V 3.9
% 0.74/0.94 SPASS beiseite: Proof found.
% 0.74/0.94 % SZS status Theorem
% 0.74/0.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.74/0.94 SPASS derived 1029 clauses, backtracked 0 clauses, performed 0 splits and kept 784 clauses.
% 0.74/0.94 SPASS allocated 86375 KBytes.
% 0.74/0.94 SPASS spent 0:00:00.59 on the problem.
% 0.74/0.94 0:00:00.04 for the input.
% 0.74/0.94 0:00:00.03 for the FLOTTER CNF translation.
% 0.74/0.94 0:00:00.11 for inferences.
% 0.74/0.94 0:00:00.00 for the backtracking.
% 0.74/0.94 0:00:00.38 for the reduction.
% 0.74/0.94
% 0.74/0.94
% 0.74/0.94 Here is a proof with depth 8, length 20 :
% 0.74/0.94 % SZS output start Refutation
% See solution above
% 0.74/0.94 Formulae used in the proof : axiom_025 axiom_026 goal_032 axiom_029 axiom_031 axiom_027
% 0.74/0.94
%------------------------------------------------------------------------------