TSTP Solution File: SET616+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:27:30 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 7 unt; 4 nHn; 18 RR)
% Number of literals : 33 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(skc3,skc2),
file('SET616+3.p',unknown),
[] ).
cnf(3,axiom,
equal(difference(skc3,skc2),difference(skc2,skc3)),
file('SET616+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,difference(v,w))
| member(u,v) ),
file('SET616+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| ~ member(u,difference(w,v)) ),
file('SET616+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| member(u,w)
| member(u,difference(v,w)) ),
file('SET616+3.p',unknown),
[] ).
cnf(15,axiom,
( equal(u,v)
| member(skf3(v,u),v)
| member(skf3(v,u),u) ),
file('SET616+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(skf3(u,v),u)
| ~ member(skf3(u,v),v)
| equal(v,u) ),
file('SET616+3.p',unknown),
[] ).
cnf(20,plain,
( ~ member(skf3(skc2,skc3),skc2)
| ~ member(skf3(skc2,skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[17,2]),
[iquote('0:Res:17.2,2.0')] ).
cnf(22,plain,
( member(skf3(skc2,skc3),skc2)
| member(skf3(skc2,skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[15,2]),
[iquote('0:Res:15.2,2.0')] ).
cnf(41,plain,
( ~ member(u,difference(skc2,skc3))
| member(u,skc3) ),
inference(spl,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpL:3.0,7.0')] ).
cnf(43,plain,
~ member(u,difference(skc2,skc3)),
inference(mrr,[status(thm)],[41,9]),
[iquote('0:MRR:41.1,9.0')] ).
cnf(78,plain,
( ~ member(u,skc3)
| member(u,skc2)
| member(u,difference(skc2,skc3)) ),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.2')] ).
cnf(81,plain,
( ~ member(u,skc2)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[14,43]),
[iquote('0:Res:14.2,43.0')] ).
cnf(84,plain,
( ~ member(u,skc3)
| member(u,skc2) ),
inference(mrr,[status(thm)],[78,9]),
[iquote('0:MRR:78.2,9.1')] ).
cnf(93,plain,
member(skf3(skc2,skc3),skc3),
inference(mrr,[status(thm)],[22,81]),
[iquote('0:MRR:22.0,81.0')] ).
cnf(94,plain,
~ member(skf3(skc2,skc3),skc2),
inference(mrr,[status(thm)],[20,81]),
[iquote('0:MRR:20.1,81.1')] ).
cnf(114,plain,
member(skf3(skc2,skc3),skc2),
inference(res,[status(thm),theory(equality)],[93,84]),
[iquote('0:Res:93.0,84.0')] ).
cnf(118,plain,
$false,
inference(mrr,[status(thm)],[114,94]),
[iquote('0:MRR:114.0,94.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 04:34:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 83 clauses, backtracked 5 clauses, performed 4 splits and kept 85 clauses.
% 0.18/0.44 SPASS allocated 85386 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.44 0:00:00.03 for the input.
% 0.18/0.44 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.01 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 2, length 18 :
% 0.18/0.44 % SZS output start Refutation
% See solution above
% 0.18/0.44 Formulae used in the proof : prove_th90 difference_defn member_equal
% 0.18/0.44
%------------------------------------------------------------------------------