%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 05:24:45 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 10 unt; 7 nHn; 28 RR)
% Number of literals : 53 ( 0 equ; 23 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(union(u,v),union(v,u)),
file('SET173+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET173+3.p',unknown),
[] ).
cnf(6,axiom,
~ equal(intersection(skc3,union(skc3,skc2)),skc3),
file('SET173+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET173+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET173+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET173+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET173+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET173+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET173+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET173+3.p',unknown),
[] ).
cnf(21,plain,
~ equal(intersection(skc3,union(skc2,skc3)),skc3),
inference(rew,[status(thm),theory(equality)],[4,6]),
[iquote('0:Rew:4.0,6.0')] ).
cnf(22,plain,
( ~ subset(skc3,intersection(skc3,union(skc2,skc3)))
| ~ subset(intersection(skc3,union(skc2,skc3)),skc3) ),
inference(res,[status(thm),theory(equality)],[13,21]),
[iquote('0:Res:13.2,21.0')] ).
cnf(41,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[9,12]),
[iquote('0:Res:9.1,12.0')] ).
cnf(46,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[7,11]),
[iquote('0:Res:7.1,11.0')] ).
cnf(52,plain,
( ~ subset(u,v)
| subset(u,w)
| member(skf2(w,u),v) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.1,14.0')] ).
cnf(63,plain,
( subset(intersection(u,v),v)
| subset(w,v) ),
inference(res,[status(thm),theory(equality)],[46,12]),
[iquote('0:Res:46.1,12.0')] ).
cnf(68,plain,
subset(intersection(u,v),v),
inference(con,[status(thm)],[63]),
[iquote('0:Con:63.1')] ).
cnf(69,plain,
subset(intersection(u,v),u),
inference(spr,[status(thm),theory(equality)],[5,68]),
[iquote('0:SpR:5.0,68.0')] ).
cnf(72,plain,
~ subset(skc3,intersection(skc3,union(skc2,skc3))),
inference(mrr,[status(thm)],[22,69]),
[iquote('0:MRR:22.1,69.0')] ).
cnf(79,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)],[18,12]),
[iquote('0:Res:18.2,12.0')] ).
cnf(143,plain,
( subset(u,union(v,u))
| subset(w,union(v,u)) ),
inference(res,[status(thm),theory(equality)],[7,41]),
[iquote('0:Res:7.1,41.0')] ).
cnf(152,plain,
subset(u,union(v,u)),
inference(con,[status(thm)],[143]),
[iquote('0:Con:143.1')] ).
cnf(862,plain,
( ~ member(skf2(intersection(u,v),u),v)
| subset(u,intersection(u,v))
| subset(w,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[7,79]),
[iquote('0:Res:7.1,79.0')] ).
cnf(881,plain,
( ~ member(skf2(intersection(u,v),u),v)
| subset(u,intersection(u,v)) ),
inference(con,[status(thm)],[862]),
[iquote('0:Con:862.2')] ).
cnf(904,plain,
( ~ subset(u,v)
| subset(u,intersection(u,v))
| subset(u,intersection(u,v)) ),
inference(res,[status(thm),theory(equality)],[52,881]),
[iquote('0:Res:52.2,881.0')] ).
cnf(914,plain,
( ~ subset(u,v)
| subset(u,intersection(u,v)) ),
inference(obv,[status(thm),theory(equality)],[904]),
[iquote('0:Obv:904.1')] ).
cnf(1014,plain,
~ subset(skc3,union(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[914,72]),
[iquote('0:Res:914.1,72.0')] ).
cnf(1024,plain,
$false,
inference(mrr,[status(thm)],[1014,152]),
[iquote('0:MRR:1014.0,152.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 09:54:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 816 clauses, backtracked 0 clauses, performed 0 splits and kept 339 clauses.
% 0.20/0.55 SPASS allocated 85881 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.55 0:00:00.04 for the input.
% 0.20/0.55 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.01 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.08 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 4, length 28 :
% 0.20/0.55 % SZS output start Refutation
% See solution above
% 0.20/0.55 Formulae used in the proof : commutativity_of_union commutativity_of_intersection prove_absorbtion_for_intersection subset_defn union_defn intersection_defn equal_defn
% 0.20/0.55
%------------------------------------------------------------------------------