TSTP Solution File: SET185+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:24:51 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 6 unt; 7 nHn; 21 RR)
% Number of literals : 41 ( 0 equ; 14 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,
subset(skc2,skc3),
file('SET185+3.p',unknown),
[] ).
cnf(3,axiom,
~ equal(union(skc2,skc3),skc3),
file('SET185+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET185+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET185+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET185+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET185+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET185+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET185+3.p',unknown),
[] ).
cnf(19,plain,
( ~ member(u,skc2)
| member(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(21,plain,
( ~ subset(skc3,union(skc2,skc3))
| ~ subset(union(skc2,skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.2,3.0')] ).
cnf(36,plain,
( ~ member(skf2(skc3,u),skc2)
| subset(v,skc3) ),
inference(res,[status(thm),theory(equality)],[19,10]),
[iquote('0:Res:19.1,10.0')] ).
cnf(37,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.1,10.0')] ).
cnf(65,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)],[7,15]),
[iquote('0:Res:7.1,15.0')] ).
cnf(106,plain,
( subset(u,union(v,u))
| subset(w,union(v,u)) ),
inference(res,[status(thm),theory(equality)],[7,37]),
[iquote('0:Res:7.1,37.0')] ).
cnf(109,plain,
subset(u,union(v,u)),
inference(con,[status(thm)],[106]),
[iquote('0:Con:106.1')] ).
cnf(110,plain,
~ subset(union(skc2,skc3),skc3),
inference(mrr,[status(thm)],[21,109]),
[iquote('0:MRR:21.0,109.0')] ).
cnf(265,plain,
( subset(union(skc2,u),skc3)
| member(skf2(skc3,union(skc2,u)),u)
| subset(v,skc3) ),
inference(res,[status(thm),theory(equality)],[65,36]),
[iquote('0:Res:65.1,36.0')] ).
cnf(275,plain,
( subset(union(skc2,u),skc3)
| member(skf2(skc3,union(skc2,u)),u) ),
inference(con,[status(thm)],[265]),
[iquote('0:Con:265.2')] ).
cnf(409,plain,
( subset(union(skc2,skc3),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[275,10]),
[iquote('0:Res:275.1,10.0')] ).
cnf(411,plain,
subset(union(skc2,skc3),skc3),
inference(con,[status(thm)],[409]),
[iquote('0:Con:409.1')] ).
cnf(412,plain,
$false,
inference(mrr,[status(thm)],[411,110]),
[iquote('0:MRR:411.0,110.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 10:55:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 359 clauses, backtracked 0 clauses, performed 0 splits and kept 211 clauses.
% 0.18/0.48 SPASS allocated 85469 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.48 0:00:00.03 for the input.
% 0.18/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.04 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 4, length 21 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : prove_subset_union subset_defn union_defn equal_defn
% 0.18/0.48
%------------------------------------------------------------------------------