%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 4 unt; 0 nHn; 15 RR)
% Number of literals : 28 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
nf(var(u)),
file('SWX222+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ nf(u)
| nf(lam(u)) ),
file('SWX222+1.p',unknown),
[] ).
cnf(29,axiom,
equal(index(cons(u,v),zero),just(u)),
file('SWX222+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ nf(u)
| ~ tc(nil,u,arr(a,arr(b,b))) ),
file('SWX222+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ tc(cons(u,v),w,x)
| tc(v,lam(w),arr(u,x)) ),
file('SWX222+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ equal(u,v)
| ~ equal(index(w,x),just(u))
| tc(w,var(x),v) ),
file('SWX222+1.p',unknown),
[] ).
cnf(60,plain,
( ~ nf(lam(u))
| ~ tc(cons(a,nil),u,arr(b,b)) ),
inference(res,[status(thm),theory(equality)],[39,31]),
[iquote('0:Res:39.1,31.1')] ).
cnf(64,plain,
( ~ nf(u)
| ~ tc(cons(a,nil),u,arr(b,b)) ),
inference(sor,[status(thm)],[60,22]),
[iquote('0:SoR:60.0,22.1')] ).
cnf(65,plain,
( ~ nf(lam(u))
| ~ tc(cons(b,cons(a,nil)),u,b) ),
inference(res,[status(thm),theory(equality)],[39,64]),
[iquote('0:Res:39.1,64.1')] ).
cnf(66,plain,
( ~ nf(u)
| ~ tc(cons(b,cons(a,nil)),u,b) ),
inference(sor,[status(thm)],[65,22]),
[iquote('0:SoR:65.0,22.1')] ).
cnf(73,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(78,plain,
( ~ equal(u,v)
| tc(cons(u,w),var(zero),v) ),
inference(eqr,[status(thm),theory(equality)],[73]),
[iquote('0:EqR:73.1')] ).
cnf(81,plain,
( ~ nf(var(zero))
| ~ equal(b,b) ),
inference(res,[status(thm),theory(equality)],[78,66]),
[iquote('0:Res:78.1,66.1')] ).
cnf(82,plain,
~ nf(var(zero)),
inference(obv,[status(thm),theory(equality)],[81]),
[iquote('0:Obv:81.1')] ).
cnf(83,plain,
$false,
inference(ssi,[status(thm)],[82,1]),
[iquote('0:SSi:82.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_spass %d %s
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue May 5 12:32:47 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 35 clauses, backtracked 0 clauses, performed 0 splits and kept 54 clauses.
% 0.18/0.40 SPASS allocated 97754 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 5, length 15 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.40 Formulae used in the proof : axiom_027 axiom_026 axiom_029 goal_036 axiom_033 axiom_035
% 0.18/0.40
%------------------------------------------------------------------------------