%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO613-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : 600s
% DateTime : Thu Jul 21 19:55:05 EDT 2022
% Result : Unsatisfiable 1.06s 1.30s
% Output : Refutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 26 ( 13 unt; 0 nHn; 26 RR)
% Number of literals : 105 ( 0 equ; 91 neg)
% Maximal clause size : 23 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
le(u,u),
file('SYO613-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ le(max(u,v),w)
| le(u,w) ),
file('SYO613-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le(max(u,v),w)
| le(v,w) ),
file('SYO613-1.p',unknown),
[] ).
cnf(4,axiom,
eq(f(u),a0),
file('SYO613-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ eq(f(u),a0)
| ~ eq(f(v),a0)
| ~ eq(f(w),a0)
| ~ eq(f(x),a0)
| ~ eq(f(y),a0)
| ~ eq(f(z),a0)
| ~ eq(f(x1),a0)
| ~ eq(f(x2),a0)
| ~ eq(f(x3),a0)
| ~ eq(f(x4),a0)
| ~ eq(f(x5),a0)
| ~ eq(f(x6),a0)
| ~ le(s(u),v)
| ~ le(s(v),w)
| ~ le(s(w),x)
| ~ le(s(x),y)
| ~ le(s(y),z)
| ~ le(s(z),x1)
| ~ le(s(x1),x2)
| ~ le(s(x2),x3)
| ~ le(s(x3),x4)
| ~ le(s(x4),x5)
| ~ le(s(x5),x6) ),
file('SYO613-1.p',unknown),
[] ).
cnf(6,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z)
| ~ le(s(x2),x1)
| ~ le(s(x3),x2)
| ~ le(s(x4),x3)
| ~ le(s(x5),x4)
| ~ le(s(x6),x5) ),
inference(mrr,[status(thm)],[5,4]),
[iquote('0:MRR:5.0,5.1,5.2,5.3,5.4,5.5,5.6,5.7,5.8,5.9,5.10,5.11,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0,4.0')] ).
cnf(9,plain,
le(u,max(u,v)),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(11,plain,
le(u,max(max(u,v),w)),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.0,2.0')] ).
cnf(12,plain,
le(u,max(max(v,u),w)),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.0,3.0')] ).
cnf(24,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z)
| ~ le(s(x2),x1)
| ~ le(s(x3),x2)
| ~ le(s(x4),x3)
| ~ le(s(x5),x4) ),
inference(res,[status(thm),theory(equality)],[11,6]),
[iquote('0:Res:11.0,6.0')] ).
cnf(26,plain,
le(u,max(max(v,max(w,u)),x)),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.0,3.0')] ).
cnf(42,plain,
le(u,max(max(v,max(w,max(x,u))),y)),
inference(res,[status(thm),theory(equality)],[26,3]),
[iquote('0:Res:26.0,3.0')] ).
cnf(57,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z)
| ~ le(s(x2),x1)
| ~ le(s(x3),x2)
| ~ le(s(x4),x3) ),
inference(res,[status(thm),theory(equality)],[26,24]),
[iquote('0:Res:26.0,24.0')] ).
cnf(89,plain,
le(u,max(max(v,max(w,max(x,max(y,u)))),z)),
inference(res,[status(thm),theory(equality)],[42,3]),
[iquote('0:Res:42.0,3.0')] ).
cnf(129,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z)
| ~ le(s(x2),x1)
| ~ le(s(x3),x2) ),
inference(res,[status(thm),theory(equality)],[42,57]),
[iquote('0:Res:42.0,57.0')] ).
cnf(187,plain,
le(u,max(max(v,max(w,max(x,max(y,max(z,u))))),x1)),
inference(res,[status(thm),theory(equality)],[89,3]),
[iquote('0:Res:89.0,3.0')] ).
cnf(250,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z)
| ~ le(s(x2),x1) ),
inference(res,[status(thm),theory(equality)],[89,129]),
[iquote('0:Res:89.0,129.0')] ).
cnf(378,plain,
le(u,max(max(v,max(w,max(x,max(y,max(z,max(x1,u)))))),x2)),
inference(res,[status(thm),theory(equality)],[187,3]),
[iquote('0:Res:187.0,3.0')] ).
cnf(505,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y)
| ~ le(s(x1),z) ),
inference(res,[status(thm),theory(equality)],[187,250]),
[iquote('0:Res:187.0,250.0')] ).
cnf(761,plain,
le(u,max(max(v,max(w,max(x,max(y,max(z,max(x1,max(x2,u))))))),x3)),
inference(res,[status(thm),theory(equality)],[378,3]),
[iquote('0:Res:378.0,3.0')] ).
cnf(1019,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x)
| ~ le(s(z),y) ),
inference(res,[status(thm),theory(equality)],[378,505]),
[iquote('0:Res:378.0,505.0')] ).
cnf(2052,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w)
| ~ le(s(y),x) ),
inference(res,[status(thm),theory(equality)],[761,1019]),
[iquote('0:Res:761.0,1019.0')] ).
cnf(2053,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w) ),
inference(res,[status(thm),theory(equality)],[1,2052]),
[iquote('0:Res:1.0,2052.0')] ).
cnf(2568,plain,
( ~ le(s(u),v)
| ~ le(s(w),u) ),
inference(res,[status(thm),theory(equality)],[1,2053]),
[iquote('0:Res:1.0,2053.0')] ).
cnf(3083,plain,
~ le(s(u),v),
inference(res,[status(thm),theory(equality)],[1,2568]),
[iquote('0:Res:1.0,2568.0')] ).
cnf(3598,plain,
$false,
inference(unc,[status(thm)],[3083,761]),
[iquote('0:UnC:3083.0,761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO613-1 : TPTP v8.1.0. Released v7.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 19:26:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.06/1.30
% 1.06/1.30 SPASS V 3.9
% 1.06/1.30 SPASS beiseite: Proof found.
% 1.06/1.30 % SZS status Theorem
% 1.06/1.30 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.06/1.30 SPASS derived 3591 clauses, backtracked 0 clauses, performed 0 splits and kept 1559 clauses.
% 1.06/1.30 SPASS allocated 67167 KBytes.
% 1.06/1.30 SPASS spent 0:00:00.86 on the problem.
% 1.06/1.30 0:00:00.03 for the input.
% 1.06/1.30 0:00:00.00 for the FLOTTER CNF translation.
% 1.06/1.30 0:00:00.10 for inferences.
% 1.06/1.30 0:00:00.00 for the backtracking.
% 1.06/1.30 0:00:00.64 for the reduction.
% 1.06/1.30
% 1.06/1.30
% 1.06/1.30 Here is a proof with depth 12, length 26 :
% 1.06/1.30 % SZS output start Refutation
% See solution above
% 1.06/1.30 Formulae used in the proof : sos_01 sos_02 sos_03 sos_04 sos_05
% 1.06/1.30
%------------------------------------------------------------------------------