%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO612-1 : TPTP v8.1.0. Released v7.1.0.
% 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 : 600s
% DateTime : Thu Jul 21 19:55:04 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 47 ( 0 equ; 36 neg)
% Maximal clause size : 13 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
le(u,u),
file('SYO612-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ le(max(u,v),w)
| le(u,w) ),
file('SYO612-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le(max(u,v),w)
| le(v,w) ),
file('SYO612-1.p',unknown),
[] ).
cnf(4,axiom,
eq(f(u),a0),
file('SYO612-1.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)
| ~ le(s(u),v)
| ~ le(s(v),w)
| ~ le(s(w),x)
| ~ le(s(x),y)
| ~ le(s(y),z)
| ~ le(s(z),x1) ),
file('SYO612-1.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) ),
inference(mrr,[status(thm)],[5,4]),
[iquote('0:MRR:5.0,5.1,5.2,5.3,5.4,5.5,5.6,4.0,4.0,4.0,4.0,4.0,4.0,4.0')] ).
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) ),
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) ),
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(96,plain,
( ~ le(s(u),v)
| ~ le(s(w),u)
| ~ le(s(x),w) ),
inference(res,[status(thm),theory(equality)],[1,57]),
[iquote('0:Res:1.0,57.0')] ).
cnf(188,plain,
( ~ le(s(u),v)
| ~ le(s(w),u) ),
inference(res,[status(thm),theory(equality)],[1,96]),
[iquote('0:Res:1.0,96.0')] ).
cnf(251,plain,
~ le(s(u),v),
inference(res,[status(thm),theory(equality)],[1,188]),
[iquote('0:Res:1.0,188.0')] ).
cnf(314,plain,
$false,
inference(unc,[status(thm)],[251,89]),
[iquote('0:UnC:251.0,89.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO612-1 : TPTP v8.1.0. Released v7.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.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 23:59:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 307 clauses, backtracked 0 clauses, performed 0 splits and kept 198 clauses.
% 0.19/0.45 SPASS allocated 63452 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.01 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.02 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 7, length 18 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : sos_01 sos_02 sos_03 sos_04 sos_05
% 0.19/0.45
%------------------------------------------------------------------------------