TSTP Solution File: SET584+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:27:08 EDT 2022
% Result : Theorem 0.19s 0.55s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 18 ( 4 unt; 6 nHn; 18 RR)
% Number of literals : 36 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc3,skc4),
file('SET584+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(union(skc3,skc5),union(skc4,skc5)),
file('SET584+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET584+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,v)
| member(u,union(v,w)) ),
file('SET584+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET584+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET584+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET584+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET584+3.p',unknown),
[] ).
cnf(15,plain,
( ~ member(u,skc3)
| member(u,skc4) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(27,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,8]),
[iquote('0:Res:7.1,8.0')] ).
cnf(28,plain,
( ~ member(skf2(union(u,v),w),u)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.1,8.0')] ).
cnf(49,plain,
( subset(union(u,v),w)
| member(skf2(w,union(u,v)),u)
| member(skf2(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.1,12.0')] ).
cnf(101,plain,
( ~ member(skf2(union(skc4,u),v),skc3)
| subset(w,union(skc4,u)) ),
inference(res,[status(thm),theory(equality)],[15,28]),
[iquote('0:Res:15.1,28.0')] ).
cnf(357,plain,
( subset(union(u,v),union(w,v))
| member(skf2(union(w,v),union(u,v)),u)
| subset(x,union(w,v)) ),
inference(res,[status(thm),theory(equality)],[49,27]),
[iquote('0:Res:49.2,27.0')] ).
cnf(362,plain,
( subset(union(u,v),union(w,v))
| member(skf2(union(w,v),union(u,v)),u) ),
inference(con,[status(thm)],[357]),
[iquote('0:Con:357.2')] ).
cnf(976,plain,
( subset(union(skc3,u),union(skc4,u))
| subset(v,union(skc4,u)) ),
inference(res,[status(thm),theory(equality)],[362,101]),
[iquote('0:Res:362.1,101.0')] ).
cnf(981,plain,
subset(union(skc3,u),union(skc4,u)),
inference(con,[status(thm)],[976]),
[iquote('0:Con:976.1')] ).
cnf(982,plain,
$false,
inference(unc,[status(thm)],[981,4]),
[iquote('0:UnC:981.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET584+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n012.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 : Sun Jul 10 02:59:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.55
% 0.19/0.55 SPASS V 3.9
% 0.19/0.55 SPASS beiseite: Proof found.
% 0.19/0.55 % SZS status Theorem
% 0.19/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.55 SPASS derived 828 clauses, backtracked 43 clauses, performed 1 splits and kept 382 clauses.
% 0.19/0.55 SPASS allocated 85849 KBytes.
% 0.19/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.19/0.55 0:00:00.04 for the input.
% 0.19/0.55 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.55 0:00:00.01 for inferences.
% 0.19/0.55 0:00:00.00 for the backtracking.
% 0.19/0.55 0:00:00.09 for the reduction.
% 0.19/0.55
% 0.19/0.55
% 0.19/0.55 Here is a proof with depth 3, length 18 :
% 0.19/0.55 % SZS output start Refutation
% See solution above
% 0.19/0.55 Formulae used in the proof : prove_th33 subset_defn union_defn
% 0.19/0.55
%------------------------------------------------------------------------------