TSTP Solution File: SET794+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Tue Jul 19 05:28:43 EDT 2022
% Result : Theorem 0.61s 0.82s
% Output : Refutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 10 unt; 8 nHn; 24 RR)
% Number of literals : 50 ( 0 equ; 22 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
total_order(skc3,skc4),
file('SET794+4.p',unknown),
[] ).
cnf(2,axiom,
min(skc5,skc3,skc4),
file('SET794+4.p',unknown),
[] ).
cnf(3,axiom,
~ least(skc5,skc3,skc4),
file('SET794+4.p',unknown),
[] ).
cnf(13,axiom,
( ~ min(u,v,w)
| member(u,w) ),
file('SET794+4.p',unknown),
[] ).
cnf(34,axiom,
( ~ member(u,v)
| member(skf27(v,w,x),v)
| least(u,y,v) ),
file('SET794+4.p',unknown),
[] ).
cnf(47,axiom,
( ~ member(u,v)
| ~ apply(w,u,skf27(v,u,w))
| least(u,w,v) ),
file('SET794+4.p',unknown),
[] ).
cnf(49,axiom,
( ~ member(u,v)
| ~ min(w,x,v)
| ~ apply(x,u,w)
| equal(w,u) ),
file('SET794+4.p',unknown),
[] ).
cnf(54,axiom,
( ~ total_order(u,v)
| ~ member(w,v)
| ~ member(x,v)
| apply(u,w,x)
| apply(u,x,w) ),
file('SET794+4.p',unknown),
[] ).
cnf(65,plain,
( ~ member(u,skc4)
| ~ member(v,skc4)
| apply(skc3,u,v)
| apply(skc3,v,u) ),
inference(res,[status(thm),theory(equality)],[1,54]),
[iquote('0:Res:1.0,54.2')] ).
cnf(66,plain,
member(skc5,skc4),
inference(res,[status(thm),theory(equality)],[2,13]),
[iquote('0:Res:2.0,13.0')] ).
cnf(67,plain,
( ~ member(u,skc4)
| ~ apply(skc3,u,skc5)
| equal(skc5,u) ),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.2')] ).
cnf(68,plain,
( ~ apply(skc3,skc5,skf27(skc4,skc5,skc3))
| ~ member(skc5,skc4) ),
inference(res,[status(thm),theory(equality)],[47,3]),
[iquote('0:Res:47.2,3.0')] ).
cnf(69,plain,
( ~ member(skc5,skc4)
| member(skf27(skc4,u,v),skc4) ),
inference(res,[status(thm),theory(equality)],[34,3]),
[iquote('0:Res:34.2,3.0')] ).
cnf(70,plain,
member(skf27(skc4,u,v),skc4),
inference(mrr,[status(thm)],[69,66]),
[iquote('0:MRR:69.0,66.0')] ).
cnf(71,plain,
~ apply(skc3,skc5,skf27(skc4,skc5,skc3)),
inference(mrr,[status(thm)],[68,66]),
[iquote('0:MRR:68.1,66.0')] ).
cnf(518,plain,
( ~ member(u,skc4)
| apply(skc3,skc5,u)
| apply(skc3,u,skc5) ),
inference(res,[status(thm),theory(equality)],[66,65]),
[iquote('0:Res:66.0,65.0')] ).
cnf(544,plain,
( apply(skc3,skc5,skc5)
| apply(skc3,skc5,skc5) ),
inference(res,[status(thm),theory(equality)],[66,518]),
[iquote('0:Res:66.0,518.0')] ).
cnf(547,plain,
( apply(skc3,skc5,skf27(skc4,u,v))
| apply(skc3,skf27(skc4,u,v),skc5) ),
inference(res,[status(thm),theory(equality)],[70,518]),
[iquote('0:Res:70.0,518.0')] ).
cnf(570,plain,
apply(skc3,skc5,skc5),
inference(obv,[status(thm),theory(equality)],[544]),
[iquote('0:Obv:544.0')] ).
cnf(1476,plain,
( ~ member(skf27(skc4,u,v),skc4)
| apply(skc3,skc5,skf27(skc4,u,v))
| equal(skf27(skc4,u,v),skc5) ),
inference(res,[status(thm),theory(equality)],[547,67]),
[iquote('0:Res:547.1,67.1')] ).
cnf(1477,plain,
( apply(skc3,skc5,skf27(skc4,u,v))
| equal(skf27(skc4,u,v),skc5) ),
inference(mrr,[status(thm)],[1476,70]),
[iquote('0:MRR:1476.0,70.0')] ).
cnf(1489,plain,
equal(skf27(skc4,skc5,skc3),skc5),
inference(res,[status(thm),theory(equality)],[1477,71]),
[iquote('0:Res:1477.0,71.0')] ).
cnf(1490,plain,
~ apply(skc3,skc5,skc5),
inference(rew,[status(thm),theory(equality)],[1489,71]),
[iquote('0:Rew:1489.0,71.0')] ).
cnf(1491,plain,
$false,
inference(mrr,[status(thm)],[1490,570]),
[iquote('0:MRR:1490.0,570.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 11:12:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.61/0.82
% 0.61/0.82 SPASS V 3.9
% 0.61/0.82 SPASS beiseite: Proof found.
% 0.61/0.82 % SZS status Theorem
% 0.61/0.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.82 SPASS derived 1216 clauses, backtracked 431 clauses, performed 18 splits and kept 961 clauses.
% 0.61/0.82 SPASS allocated 87881 KBytes.
% 0.61/0.82 SPASS spent 0:00:00.47 on the problem.
% 0.61/0.82 0:00:00.04 for the input.
% 0.61/0.82 0:00:00.18 for the FLOTTER CNF translation.
% 0.61/0.82 0:00:00.02 for inferences.
% 0.61/0.82 0:00:00.00 for the backtracking.
% 0.61/0.82 0:00:00.20 for the reduction.
% 0.61/0.82
% 0.61/0.82
% 0.61/0.82 Here is a proof with depth 5, length 24 :
% 0.61/0.82 % SZS output start Refutation
% See solution above
% 0.61/0.82 Formulae used in the proof : thIV6 min least total_order
% 0.61/0.82
%------------------------------------------------------------------------------