%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX219+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 07:07:26 PM UTC 2026
% Result : Theorem 2.44s 2.69s
% Output : Refutation 2.44s
% 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 : 51 ( 0 equ; 37 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 : 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('SWX219+1.p',unknown),
[] ).
cnf(26,axiom,
equal(index(cons(u,v),suc(w)),index(v,w)),
file('SWX219+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX219+1.p',unknown),
[] ).
cnf(33,axiom,
~ tc(nil,u,arr(arr(b,c),arr(arr(a,b),arr(a,c)))),
file('SWX219+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX219+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ tc(u,v,w)
| ~ tc(u,x,arr(w,y))
| tc(u,app(x,v,w),y) ),
file('SWX219+1.p',unknown),
[] ).
cnf(40,plain,
~ tc(cons(arr(b,c),nil),u,arr(arr(a,b),arr(a,c))),
inference(res,[status(thm),theory(equality)],[32,33]),
[iquote('0:Res:32.1,33.0')] ).
cnf(61,plain,
~ tc(cons(arr(a,b),cons(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(arr(a,b),cons(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(arr(a,b),cons(arr(b,c),nil))),u,v)
| ~ tc(cons(a,cons(arr(a,b),cons(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(86,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(87,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)],[86]),
[iquote('0:EqR:86.1')] ).
cnf(103,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)],[25,87]),
[iquote('0:SpL:25.0,87.1')] ).
cnf(151,plain,
( ~ equal(u,v)
| tc(cons(w,cons(x,cons(u,y))),var(suc(suc(zero))),v) ),
inference(eqr,[status(thm),theory(equality)],[103]),
[iquote('0:EqR:103.1')] ).
cnf(376,plain,
( ~ equal(arr(b,c),arr(u,c))
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),v,u) ),
inference(res,[status(thm),theory(equality)],[151,71]),
[iquote('0:Res:151.1,71.1')] ).
cnf(378,plain,
( ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),u,v)
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),w,arr(v,x))
| ~ equal(arr(b,c),arr(x,c)) ),
inference(res,[status(thm),theory(equality)],[36,376]),
[iquote('0:Res:36.2,376.1')] ).
cnf(1701,plain,
( ~ equal(arr(a,b),arr(u,v))
| ~ tc(cons(a,cons(arr(a,b),cons(arr(b,c),nil))),w,u)
| ~ equal(arr(b,c),arr(v,c)) ),
inference(res,[status(thm),theory(equality)],[88,378]),
[iquote('0:Res:88.1,378.1')] ).
cnf(2912,plain,
( ~ equal(a,u)
| ~ equal(arr(a,b),arr(u,v))
| ~ equal(arr(b,c),arr(v,c)) ),
inference(res,[status(thm),theory(equality)],[76,1701]),
[iquote('0:Res:76.1,1701.1')] ).
cnf(2916,plain,
( ~ equal(a,a)
| ~ equal(arr(b,c),arr(b,c)) ),
inference(eqr,[status(thm),theory(equality)],[2912]),
[iquote('0:EqR:2912.1')] ).
cnf(2917,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2916]),
[iquote('0:Obv:2916.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX219+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.15/0.33 % Computer : n027.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 12:22:04 EDT 2026
% 0.15/0.34 % CPUTime :
% 2.44/2.69
% 2.44/2.69 SPASS V 3.9
% 2.44/2.69 SPASS beiseite: Proof found.
% 2.44/2.69 % SZS status Theorem
% 2.44/2.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.44/2.69 SPASS derived 2709 clauses, backtracked 0 clauses, performed 0 splits and kept 1954 clauses.
% 2.44/2.69 SPASS allocated 88085 KBytes.
% 2.44/2.69 SPASS spent 0:00:02.33 on the problem.
% 2.44/2.69 0:00:00.03 for the input.
% 2.44/2.69 0:00:00.03 for the FLOTTER CNF translation.
% 2.44/2.69 0:00:00.61 for inferences.
% 2.44/2.69 0:00:00.00 for the backtracking.
% 2.44/2.69 0:00:01.59 for the reduction.
% 2.44/2.69
% 2.44/2.69
% 2.44/2.69 Here is a proof with depth 9, length 24 :
% 2.44/2.69 % SZS output start Refutation
% See solution above
% 2.44/2.69 Formulae used in the proof : axiom_025 axiom_026 axiom_029 goal_032 axiom_031 axiom_027
% 2.44/2.69
%------------------------------------------------------------------------------