%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET809+4 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Jul 19 05:28:48 EDT 2022
% Result : Theorem 0.36s 0.53s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 16 RR)
% Number of literals : 30 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(skc1,on),
file('SET809+4.p',unknown),
[] ).
cnf(2,axiom,
member(skc1,skc1),
file('SET809+4.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,on)
| strict_well_order(member_predicate,u) ),
file('SET809+4.p',unknown),
[] ).
cnf(11,axiom,
( ~ strict_well_order(u,v)
| strict_order(u,v) ),
file('SET809+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ strict_order(u,v)
| skP0(u,v) ),
file('SET809+4.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(u,v)
| apply(member_predicate,u,v) ),
file('SET809+4.p',unknown),
[] ).
cnf(66,axiom,
( ~ member(u,v)
| ~ member(w,v)
| ~ skP0(x,v)
| ~ apply(x,u,w)
| ~ apply(x,w,u) ),
file('SET809+4.p',unknown),
[] ).
cnf(78,plain,
apply(member_predicate,skc1,skc1),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.0')] ).
cnf(85,plain,
( ~ member(u,skc1)
| ~ skP0(v,skc1)
| ~ apply(v,u,skc1)
| ~ apply(v,skc1,u) ),
inference(res,[status(thm),theory(equality)],[2,66]),
[iquote('0:Res:2.0,66.1')] ).
cnf(92,plain,
strict_well_order(member_predicate,skc1),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(143,plain,
( ~ skP0(u,skc1)
| ~ apply(u,skc1,skc1)
| ~ apply(u,skc1,skc1) ),
inference(res,[status(thm),theory(equality)],[2,85]),
[iquote('0:Res:2.0,85.3')] ).
cnf(148,plain,
( ~ skP0(u,skc1)
| ~ apply(u,skc1,skc1) ),
inference(obv,[status(thm),theory(equality)],[143]),
[iquote('0:Obv:143.1')] ).
cnf(225,plain,
~ skP0(member_predicate,skc1),
inference(res,[status(thm),theory(equality)],[78,148]),
[iquote('0:Res:78.0,148.1')] ).
cnf(227,plain,
~ strict_order(member_predicate,skc1),
inference(res,[status(thm),theory(equality)],[12,225]),
[iquote('0:Res:12.1,225.0')] ).
cnf(229,plain,
~ strict_well_order(member_predicate,skc1),
inference(res,[status(thm),theory(equality)],[11,227]),
[iquote('0:Res:11.1,227.0')] ).
cnf(230,plain,
$false,
inference(mrr,[status(thm)],[229,92]),
[iquote('0:MRR:229.0,92.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET809+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 : Sun Jul 10 22:33:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.36/0.53
% 0.36/0.53 SPASS V 3.9
% 0.36/0.53 SPASS beiseite: Proof found.
% 0.36/0.53 % SZS status Theorem
% 0.36/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.53 SPASS derived 159 clauses, backtracked 0 clauses, performed 2 splits and kept 168 clauses.
% 0.36/0.53 SPASS allocated 99265 KBytes.
% 0.36/0.53 SPASS spent 0:00:00.19 on the problem.
% 0.36/0.53 0:00:00.04 for the input.
% 0.36/0.53 0:00:00.12 for the FLOTTER CNF translation.
% 0.36/0.53 0:00:00.00 for inferences.
% 0.36/0.53 0:00:00.00 for the backtracking.
% 0.36/0.53 0:00:00.01 for the reduction.
% 0.36/0.53
% 0.36/0.53
% 0.36/0.53 Here is a proof with depth 5, length 16 :
% 0.36/0.53 % SZS output start Refutation
% See solution above
% 0.36/0.53 Formulae used in the proof : thV2 ordinal_number strict_well_order subset empty_set strict_order rel_member
% 0.36/0.53
%------------------------------------------------------------------------------