TSTP Solution File: SET586+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 05:27:09 EDT 2022
% Result : Theorem 0.52s 0.75s
% Output : Refutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 5 unt; 6 nHn; 20 RR)
% Number of literals : 41 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 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('SET586+3.p',unknown),
[] ).
cnf(3,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET586+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(intersection(skc3,skc5),intersection(skc4,skc5)),
file('SET586+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET586+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET586+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET586+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET586+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET586+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET586+3.p',unknown),
[] ).
cnf(29,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.1,7.0')] ).
cnf(32,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.1,6.0')] ).
cnf(50,plain,
( ~ member(skf2(intersection(u,v),w),u)
| ~ member(skf2(intersection(u,v),w),v)
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.2,8.0')] ).
cnf(84,plain,
( ~ subset(u,v)
| subset(intersection(u,w),x)
| member(skf2(x,intersection(u,w)),v) ),
inference(res,[status(thm),theory(equality)],[32,9]),
[iquote('0:Res:32.1,9.0')] ).
cnf(405,plain,
( ~ member(skf2(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v))
| subset(x,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[29,50]),
[iquote('0:Res:29.1,50.0')] ).
cnf(411,plain,
( ~ member(skf2(intersection(u,v),intersection(w,u)),v)
| subset(intersection(w,u),intersection(u,v)) ),
inference(con,[status(thm)],[405]),
[iquote('0:Con:405.2')] ).
cnf(1256,plain,
( ~ subset(u,v)
| subset(intersection(u,w),intersection(w,v))
| subset(intersection(u,w),intersection(w,v)) ),
inference(res,[status(thm),theory(equality)],[84,411]),
[iquote('0:Res:84.2,411.0')] ).
cnf(1268,plain,
( ~ subset(u,v)
| subset(intersection(u,w),intersection(w,v)) ),
inference(obv,[status(thm),theory(equality)],[1256]),
[iquote('0:Obv:1256.1')] ).
cnf(1494,plain,
( ~ subset(u,v)
| subset(intersection(u,w),intersection(v,w)) ),
inference(spr,[status(thm),theory(equality)],[3,1268]),
[iquote('0:SpR:3.0,1268.1')] ).
cnf(1694,plain,
~ subset(skc3,skc4),
inference(res,[status(thm),theory(equality)],[1494,4]),
[iquote('0:Res:1494.1,4.0')] ).
cnf(1695,plain,
$false,
inference(mrr,[status(thm)],[1694,1]),
[iquote('0:MRR:1694.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 07:24:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.52/0.75
% 0.52/0.75 SPASS V 3.9
% 0.52/0.75 SPASS beiseite: Proof found.
% 0.52/0.75 % SZS status Theorem
% 0.52/0.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.75 SPASS derived 1451 clauses, backtracked 31 clauses, performed 1 splits and kept 701 clauses.
% 0.52/0.75 SPASS allocated 86523 KBytes.
% 0.52/0.75 SPASS spent 0:00:00.40 on the problem.
% 0.52/0.75 0:00:00.04 for the input.
% 0.52/0.75 0:00:00.03 for the FLOTTER CNF translation.
% 0.52/0.75 0:00:00.02 for inferences.
% 0.52/0.75 0:00:00.00 for the backtracking.
% 0.52/0.75 0:00:00.29 for the reduction.
% 0.52/0.75
% 0.52/0.75
% 0.52/0.75 Here is a proof with depth 5, length 20 :
% 0.52/0.75 % SZS output start Refutation
% See solution above
% 0.52/0.75 Formulae used in the proof : prove_intersection_of_subset commutativity_of_intersection subset_defn intersection_defn
% 0.52/0.75
%------------------------------------------------------------------------------