TSTP Solution File: SYO617-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO617-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 19:55:06 EDT 2022
% Result : Unsatisfiable 0.32s 0.57s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of clauses : 40 ( 9 unt; 5 nHn; 40 RR)
% Number of literals : 81 ( 0 equ; 55 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
le(u,u),
file('SYO617-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ le(max(u,v),w)
| le(u,w) ),
file('SYO617-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le(max(u,v),w)
| le(v,w) ),
file('SYO617-1.p',unknown),
[] ).
cnf(4,axiom,
( eq(f(u),a2)
| eq(f(u),a1)
| eq(f(u),a0) ),
file('SYO617-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a0)
| ~ eq(f(u),a0) ),
file('SYO617-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a1)
| ~ eq(f(u),a1) ),
file('SYO617-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a2)
| ~ eq(f(u),a2) ),
file('SYO617-1.p',unknown),
[] ).
cnf(8,plain,
le(u,max(v,u)),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(11,plain,
le(u,max(u,v)),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(14,plain,
le(u,max(max(u,v),w)),
inference(res,[status(thm),theory(equality)],[11,2]),
[iquote('0:Res:11.0,2.0')] ).
cnf(15,plain,
le(u,max(max(v,u),w)),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.0,3.0')] ).
cnf(30,plain,
( ~ eq(f(s(u)),a2)
| ~ eq(f(u),a2) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(31,plain,
( ~ eq(f(max(u,s(v))),a2)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[8,7]),
[iquote('0:Res:8.0,7.0')] ).
cnf(38,plain,
( ~ eq(f(max(s(u),v)),a2)
| ~ eq(f(u),a2) ),
inference(res,[status(thm),theory(equality)],[11,7]),
[iquote('0:Res:11.0,7.0')] ).
cnf(39,plain,
( ~ eq(f(max(max(s(u),v),w)),a2)
| ~ eq(f(u),a2) ),
inference(res,[status(thm),theory(equality)],[14,7]),
[iquote('0:Res:14.0,7.0')] ).
cnf(53,plain,
( ~ eq(f(s(u)),a1)
| ~ eq(f(u),a1) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(54,plain,
( ~ eq(f(max(u,s(v))),a1)
| ~ eq(f(v),a1) ),
inference(res,[status(thm),theory(equality)],[8,6]),
[iquote('0:Res:8.0,6.0')] ).
cnf(61,plain,
( ~ eq(f(max(s(u),v)),a1)
| ~ eq(f(u),a1) ),
inference(res,[status(thm),theory(equality)],[11,6]),
[iquote('0:Res:11.0,6.0')] ).
cnf(63,plain,
( ~ eq(f(max(max(u,s(v)),w)),a1)
| ~ eq(f(v),a1) ),
inference(res,[status(thm),theory(equality)],[15,6]),
[iquote('0:Res:15.0,6.0')] ).
cnf(76,plain,
( ~ eq(f(s(u)),a0)
| ~ eq(f(u),a0) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(77,plain,
( ~ eq(f(max(u,s(v))),a0)
| ~ eq(f(v),a0) ),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.0,5.0')] ).
cnf(86,plain,
( ~ eq(f(max(s(u),v)),a0)
| ~ eq(f(u),a0) ),
inference(res,[status(thm),theory(equality)],[11,5]),
[iquote('0:Res:11.0,5.0')] ).
cnf(93,plain,
( ~ eq(f(u),a0)
| eq(f(s(u)),a2)
| eq(f(s(u)),a1) ),
inference(res,[status(thm),theory(equality)],[4,76]),
[iquote('0:Res:4.2,76.0')] ).
cnf(164,plain,
( ~ eq(f(u),a0)
| eq(f(max(v,s(u))),a2)
| eq(f(max(v,s(u))),a1) ),
inference(res,[status(thm),theory(equality)],[4,77]),
[iquote('0:Res:4.2,77.0')] ).
cnf(165,plain,
( ~ eq(f(u),a0)
| eq(f(max(s(u),v)),a2)
| eq(f(max(s(u),v)),a1) ),
inference(res,[status(thm),theory(equality)],[4,86]),
[iquote('0:Res:4.2,86.0')] ).
cnf(339,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(s(v),s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[164,61]),
[iquote('0:Res:164.2,61.0')] ).
cnf(341,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(max(w,s(v)),s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[164,63]),
[iquote('0:Res:164.2,63.0')] ).
cnf(742,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a2) ),
inference(res,[status(thm),theory(equality)],[341,39]),
[iquote('0:Res:341.2,39.0')] ).
cnf(746,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1) ),
inference(mrr,[status(thm)],[339,742]),
[iquote('0:MRR:339.2,742.2')] ).
cnf(760,plain,
( ~ eq(f(u),a0)
| eq(f(s(u)),a2) ),
inference(mrr,[status(thm)],[93,746]),
[iquote('0:MRR:93.2,746.1')] ).
cnf(761,plain,
( ~ eq(f(u),a0)
| eq(f(max(s(u),v)),a2) ),
inference(mrr,[status(thm)],[165,746]),
[iquote('0:MRR:165.2,746.1')] ).
cnf(778,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[761,31]),
[iquote('0:Res:761.1,31.0')] ).
cnf(786,plain,
~ eq(f(u),a0),
inference(mrr,[status(thm)],[760,778]),
[iquote('0:MRR:760.1,778.1')] ).
cnf(801,plain,
( eq(f(u),a2)
| eq(f(u),a1) ),
inference(mrr,[status(thm)],[4,786]),
[iquote('0:MRR:4.2,786.0')] ).
cnf(802,plain,
( ~ eq(f(u),a1)
| eq(f(s(u)),a2) ),
inference(res,[status(thm),theory(equality)],[801,53]),
[iquote('0:Res:801.1,53.0')] ).
cnf(803,plain,
( ~ eq(f(u),a1)
| eq(f(max(v,s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[801,54]),
[iquote('0:Res:801.1,54.0')] ).
cnf(820,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[803,38]),
[iquote('0:Res:803.1,38.0')] ).
cnf(827,plain,
~ eq(f(u),a1),
inference(mrr,[status(thm)],[802,820]),
[iquote('0:MRR:802.1,820.1')] ).
cnf(842,plain,
eq(f(u),a2),
inference(mrr,[status(thm)],[801,827]),
[iquote('0:MRR:801.1,827.0')] ).
cnf(844,plain,
$false,
inference(mrr,[status(thm)],[30,842]),
[iquote('0:MRR:30.0,30.1,842.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : SYO617-1 : TPTP v8.1.0. Released v7.1.0.
% 0.03/0.16 % Command : run_spass %d %s
% 0.11/0.35 % Computer : n003.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 600
% 0.11/0.35 % DateTime : Sat Jul 9 15:48:43 EDT 2022
% 0.11/0.36 % CPUTime :
% 0.32/0.57
% 0.32/0.57 SPASS V 3.9
% 0.32/0.57 SPASS beiseite: Proof found.
% 0.32/0.57 % SZS status Theorem
% 0.32/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.57 SPASS derived 973 clauses, backtracked 0 clauses, performed 0 splits and kept 772 clauses.
% 0.32/0.57 SPASS allocated 64688 KBytes.
% 0.32/0.57 SPASS spent 0:00:00.18 on the problem.
% 0.32/0.57 0:00:00.03 for the input.
% 0.32/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.32/0.57 0:00:00.01 for inferences.
% 0.32/0.57 0:00:00.00 for the backtracking.
% 0.32/0.57 0:00:00.10 for the reduction.
% 0.32/0.57
% 0.32/0.57
% 0.32/0.57 Here is a proof with depth 5, length 40 :
% 0.32/0.57 % SZS output start Refutation
% See solution above
% 0.32/0.57 Formulae used in the proof : sos_01 sos_02 sos_03 sos_04 sos_05 sos_06 sos_07
% 0.32/0.57
%------------------------------------------------------------------------------