TSTP Solution File: SET162+4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% 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 05:24:39 EDT 2022
% Result : Theorem 1.61s 1.79s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 6 unt; 6 nHn; 17 RR)
% Number of literals : 31 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(u,empty_set),
file('SET162+4.p',unknown),
[] ).
cnf(3,axiom,
~ equal_set(union(skc1,empty_set),skc1),
file('SET162+4.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf3(v,u),u) ),
file('SET162+4.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf3(u,v),u)
| subset(w,u) ),
file('SET162+4.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(u,v)
| member(u,union(v,w)) ),
file('SET162+4.p',unknown),
[] ).
cnf(24,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_set(v,u) ),
file('SET162+4.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET162+4.p',unknown),
[] ).
cnf(31,plain,
( ~ subset(skc1,union(skc1,empty_set))
| ~ subset(union(skc1,empty_set),skc1) ),
inference(res,[status(thm),theory(equality)],[24,3]),
[iquote('0:Res:24.2,3.0')] ).
cnf(46,plain,
( ~ member(skf3(union(u,v),w),u)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[15,12]),
[iquote('0:Res:15.1,12.0')] ).
cnf(177,plain,
( subset(union(u,v),w)
| member(skf3(w,union(u,v)),u)
| member(skf3(w,union(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[7,25]),
[iquote('0:Res:7.1,25.0')] ).
cnf(846,plain,
( subset(u,union(u,v))
| subset(w,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,46]),
[iquote('0:Res:7.1,46.0')] ).
cnf(851,plain,
subset(u,union(u,v)),
inference(con,[status(thm)],[846]),
[iquote('0:Con:846.1')] ).
cnf(852,plain,
~ subset(union(skc1,empty_set),skc1),
inference(mrr,[status(thm)],[31,851]),
[iquote('0:MRR:31.0,851.0')] ).
cnf(3228,plain,
( subset(union(u,empty_set),v)
| member(skf3(v,union(u,empty_set)),u) ),
inference(res,[status(thm),theory(equality)],[177,1]),
[iquote('0:Res:177.2,1.0')] ).
cnf(5691,plain,
( subset(union(u,empty_set),u)
| subset(v,u) ),
inference(res,[status(thm),theory(equality)],[3228,12]),
[iquote('0:Res:3228.1,12.0')] ).
cnf(5708,plain,
subset(union(u,empty_set),u),
inference(con,[status(thm)],[5691]),
[iquote('0:Con:5691.1')] ).
cnf(5709,plain,
$false,
inference(unc,[status(thm)],[5708,852]),
[iquote('0:UnC:5708.0,852.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 10:18:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.61/1.79
% 1.61/1.79 SPASS V 3.9
% 1.61/1.79 SPASS beiseite: Proof found.
% 1.61/1.79 % SZS status Theorem
% 1.61/1.79 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.61/1.79 SPASS derived 4869 clauses, backtracked 0 clauses, performed 0 splits and kept 3000 clauses.
% 1.61/1.79 SPASS allocated 89890 KBytes.
% 1.61/1.79 SPASS spent 0:00:01.40 on the problem.
% 1.61/1.79 0:00:00.03 for the input.
% 1.61/1.79 0:00:00.04 for the FLOTTER CNF translation.
% 1.61/1.79 0:00:00.06 for inferences.
% 1.61/1.79 0:00:00.00 for the backtracking.
% 1.61/1.79 0:00:01.22 for the reduction.
% 1.61/1.79
% 1.61/1.79
% 1.61/1.79 Here is a proof with depth 3, length 17 :
% 1.61/1.79 % SZS output start Refutation
% See solution above
% 1.61/1.79 Formulae used in the proof : empty_set thI18 subset union equal_set
% 1.61/1.79
%------------------------------------------------------------------------------