TSTP Solution File: SET810+4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 6.21s 6.41s
% Output : Refutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 12 unt; 0 nHn; 23 RR)
% Number of literals : 42 ( 0 equ; 26 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(skc3,on),
file('SET810+4.p',unknown),
[] ).
cnf(2,axiom,
member(skc3,skc2),
file('SET810+4.p',unknown),
[] ).
cnf(3,axiom,
member(skc2,skc3),
file('SET810+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,on)
| strict_well_order(member_predicate,u) ),
file('SET810+4.p',unknown),
[] ).
cnf(13,axiom,
( ~ strict_well_order(u,v)
| strict_order(u,v) ),
file('SET810+4.p',unknown),
[] ).
cnf(14,axiom,
( ~ strict_order(u,v)
| skP0(u,v) ),
file('SET810+4.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,v)
| apply(member_predicate,u,v) ),
file('SET810+4.p',unknown),
[] ).
cnf(38,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET810+4.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(u,v)
| ~ member(v,on)
| subset(u,v) ),
file('SET810+4.p',unknown),
[] ).
cnf(68,axiom,
( ~ member(u,v)
| ~ member(w,v)
| ~ skP0(x,v)
| ~ apply(x,u,w)
| ~ apply(x,w,u) ),
file('SET810+4.p',unknown),
[] ).
cnf(103,plain,
( ~ member(skc3,on)
| subset(skc2,skc3) ),
inference(res,[status(thm),theory(equality)],[3,40]),
[iquote('0:Res:3.0,40.0')] ).
cnf(107,plain,
apply(member_predicate,skc2,skc3),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.0,22.0')] ).
cnf(114,plain,
( ~ member(u,skc3)
| ~ skP0(v,skc3)
| ~ apply(v,u,skc2)
| ~ apply(v,skc2,u) ),
inference(res,[status(thm),theory(equality)],[3,68]),
[iquote('0:Res:3.0,68.1')] ).
cnf(131,plain,
apply(member_predicate,skc3,skc2),
inference(res,[status(thm),theory(equality)],[2,22]),
[iquote('0:Res:2.0,22.0')] ).
cnf(137,plain,
( ~ subset(skc2,u)
| member(skc3,u) ),
inference(res,[status(thm),theory(equality)],[2,38]),
[iquote('0:Res:2.0,38.1')] ).
cnf(146,plain,
subset(skc2,skc3),
inference(mrr,[status(thm)],[103,1]),
[iquote('0:MRR:103.0,1.0')] ).
cnf(150,plain,
member(skc3,skc3),
inference(res,[status(thm),theory(equality)],[146,137]),
[iquote('0:Res:146.0,137.0')] ).
cnf(17981,plain,
( ~ member(skc3,skc3)
| ~ skP0(member_predicate,skc3)
| ~ apply(member_predicate,skc2,skc3) ),
inference(res,[status(thm),theory(equality)],[131,114]),
[iquote('0:Res:131.0,114.2')] ).
cnf(17990,plain,
~ skP0(member_predicate,skc3),
inference(mrr,[status(thm)],[17981,150,107]),
[iquote('0:MRR:17981.0,17981.2,150.0,107.0')] ).
cnf(17993,plain,
~ strict_order(member_predicate,skc3),
inference(res,[status(thm),theory(equality)],[14,17990]),
[iquote('0:Res:14.1,17990.0')] ).
cnf(17994,plain,
~ strict_well_order(member_predicate,skc3),
inference(res,[status(thm),theory(equality)],[13,17993]),
[iquote('0:Res:13.1,17993.0')] ).
cnf(17995,plain,
~ member(skc3,on),
inference(res,[status(thm),theory(equality)],[12,17994]),
[iquote('0:Res:12.1,17994.0')] ).
cnf(17996,plain,
$false,
inference(mrr,[status(thm)],[17995,1]),
[iquote('0:MRR:17995.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 07:10:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.21/6.41
% 6.21/6.41 SPASS V 3.9
% 6.21/6.41 SPASS beiseite: Proof found.
% 6.21/6.41 % SZS status Theorem
% 6.21/6.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.21/6.41 SPASS derived 16246 clauses, backtracked 251 clauses, performed 23 splits and kept 7575 clauses.
% 6.21/6.41 SPASS allocated 110299 KBytes.
% 6.21/6.41 SPASS spent 0:00:05.91 on the problem.
% 6.21/6.41 0:00:00.04 for the input.
% 6.21/6.41 0:00:00.11 for the FLOTTER CNF translation.
% 6.21/6.41 0:00:00.15 for inferences.
% 6.21/6.41 0:00:00.03 for the backtracking.
% 6.21/6.41 0:00:05.44 for the reduction.
% 6.21/6.41
% 6.21/6.41
% 6.21/6.41 Here is a proof with depth 5, length 23 :
% 6.21/6.41 % SZS output start Refutation
% See solution above
% 6.21/6.41 Formulae used in the proof : thV3 ordinal_number strict_well_order subset empty_set strict_order rel_member
% 6.21/6.41
%------------------------------------------------------------------------------