TSTP Solution File: SET175+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET175+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 05:24:46 EDT 2022
% Result : Theorem 183.13s 183.36s
% Output : Refutation 183.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 28 ( 10 unt; 10 nHn; 28 RR)
% Number of literals : 53 ( 0 equ; 18 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('SET175+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET175+3.p',unknown),
[] ).
cnf(6,axiom,
~ equal(union(skc3,intersection(skc3,skc2)),skc3),
file('SET175+3.p',unknown),
[] ).
cnf(7,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET175+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET175+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET175+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET175+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET175+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET175+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET175+3.p',unknown),
[] ).
cnf(21,plain,
~ equal(union(skc3,intersection(skc2,skc3)),skc3),
inference(rew,[status(thm),theory(equality)],[5,6]),
[iquote('0:Rew:5.0,6.0')] ).
cnf(22,plain,
( ~ subset(skc3,union(skc3,intersection(skc2,skc3)))
| ~ subset(union(skc3,intersection(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(58,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)],[7,17]),
[iquote('0:Res:7.1,17.0')] ).
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(141,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(150,plain,
subset(u,union(v,u)),
inference(con,[status(thm)],[141]),
[iquote('0:Con:141.1')] ).
cnf(156,plain,
subset(u,union(u,v)),
inference(spr,[status(thm),theory(equality)],[4,150]),
[iquote('0:SpR:4.0,150.0')] ).
cnf(159,plain,
~ subset(union(skc3,intersection(skc2,skc3)),skc3),
inference(mrr,[status(thm)],[22,156]),
[iquote('0:MRR:22.0,156.0')] ).
cnf(412,plain,
( subset(union(u,v),u)
| member(skf2(u,union(u,v)),v)
| subset(w,u) ),
inference(res,[status(thm),theory(equality)],[58,12]),
[iquote('0:Res:58.1,12.0')] ).
cnf(430,plain,
( subset(union(u,v),u)
| member(skf2(u,union(u,v)),v) ),
inference(con,[status(thm)],[412]),
[iquote('0:Con:412.2')] ).
cnf(538,plain,
( ~ subset(u,v)
| subset(union(w,u),w)
| member(skf2(w,union(w,u)),v) ),
inference(res,[status(thm),theory(equality)],[430,14]),
[iquote('0:Res:430.1,14.0')] ).
cnf(85321,plain,
( ~ subset(u,v)
| subset(union(v,u),v)
| subset(w,v) ),
inference(res,[status(thm),theory(equality)],[538,12]),
[iquote('0:Res:538.2,12.0')] ).
cnf(85352,plain,
( ~ subset(u,v)
| subset(union(v,u),v) ),
inference(con,[status(thm)],[85321]),
[iquote('0:Con:85321.2')] ).
cnf(85430,plain,
~ subset(intersection(skc2,skc3),skc3),
inference(res,[status(thm),theory(equality)],[85352,159]),
[iquote('0:Res:85352.1,159.0')] ).
cnf(85491,plain,
$false,
inference(mrr,[status(thm)],[85430,68]),
[iquote('0:MRR:85430.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 11:09:16 EDT 2022
% 0.11/0.33 % CPUTime :
% 183.13/183.36
% 183.13/183.36 SPASS V 3.9
% 183.13/183.36 SPASS beiseite: Proof found.
% 183.13/183.36 % SZS status Theorem
% 183.13/183.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 183.13/183.36 SPASS derived 68642 clauses, backtracked 0 clauses, performed 0 splits and kept 20962 clauses.
% 183.13/183.36 SPASS allocated 141412 KBytes.
% 183.13/183.36 SPASS spent 0:03:01.16 on the problem.
% 183.13/183.36 0:00:00.03 for the input.
% 183.13/183.36 0:00:00.03 for the FLOTTER CNF translation.
% 183.13/183.36 0:00:00.92 for inferences.
% 183.13/183.36 0:00:00.00 for the backtracking.
% 183.13/183.36 0:2:59.71 for the reduction.
% 183.13/183.36
% 183.13/183.36
% 183.13/183.36 Here is a proof with depth 5, length 28 :
% 183.13/183.36 % SZS output start Refutation
% See solution above
% 183.13/183.36 Formulae used in the proof : commutativity_of_union commutativity_of_intersection prove_absorbtion_for_union subset_defn union_defn intersection_defn equal_defn
% 183.13/183.36
%------------------------------------------------------------------------------