TSTP Solution File: SET577+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:27:04 EDT 2022
% Result : Theorem 3.95s 4.13s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 51 ( 15 unt; 22 nHn; 51 RR)
% Number of literals : 96 ( 0 equ; 21 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(union(skc4,skc5),skc3),
file('SET577+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,skc4)
| member(u,skc3) ),
file('SET577+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,skc5)
| member(u,skc3) ),
file('SET577+3.p',unknown),
[] ).
cnf(7,axiom,
equal(union(u,v),union(v,u)),
file('SET577+3.p',unknown),
[] ).
cnf(8,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET577+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| member(u,union(v,w)) ),
file('SET577+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| member(u,union(w,v)) ),
file('SET577+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET577+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,skc3)
| member(u,skc5)
| member(u,skc4) ),
file('SET577+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal(v,u) ),
file('SET577+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(u,union(v,w))
| member(u,v)
| member(u,w) ),
file('SET577+3.p',unknown),
[] ).
cnf(20,plain,
( ~ subset(skc3,union(skc4,skc5))
| ~ subset(union(skc4,skc5),skc3) ),
inference(res,[status(thm),theory(equality)],[13,2]),
[iquote('0:Res:13.2,2.0')] ).
cnf(36,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[10,11]),
[iquote('0:Res:10.1,11.0')] ).
cnf(37,plain,
( ~ member(skf2(union(u,v),w),u)
| subset(x,union(u,v)) ),
inference(res,[status(thm),theory(equality)],[9,11]),
[iquote('0:Res:9.1,11.0')] ).
cnf(72,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)],[8,17]),
[iquote('0:Res:8.1,17.0')] ).
cnf(222,plain,
( subset(u,union(v,u))
| subset(w,union(v,u)) ),
inference(res,[status(thm),theory(equality)],[8,36]),
[iquote('0:Res:8.1,36.0')] ).
cnf(224,plain,
subset(u,union(v,u)),
inference(con,[status(thm)],[222]),
[iquote('0:Con:222.1')] ).
cnf(229,plain,
( ~ subset(union(u,v),v)
| equal(union(u,v),v) ),
inference(res,[status(thm),theory(equality)],[224,13]),
[iquote('0:Res:224.0,13.0')] ).
cnf(236,plain,
( ~ member(skf2(union(u,v),w),v)
| subset(x,union(v,u)) ),
inference(spl,[status(thm),theory(equality)],[7,37]),
[iquote('0:SpL:7.0,37.0')] ).
cnf(250,plain,
( ~ subset(union(u,v),u)
| equal(union(v,u),u) ),
inference(spl,[status(thm),theory(equality)],[7,229]),
[iquote('0:SpL:7.0,229.0')] ).
cnf(418,plain,
( subset(union(u,v),u)
| member(skf2(u,union(u,v)),v)
| subset(w,u) ),
inference(res,[status(thm),theory(equality)],[72,11]),
[iquote('0:Res:72.1,11.0')] ).
cnf(425,plain,
( subset(union(u,v),v)
| member(skf2(v,union(u,v)),u)
| subset(w,v) ),
inference(res,[status(thm),theory(equality)],[72,11]),
[iquote('0:Res:72.2,11.0')] ).
cnf(429,plain,
( subset(union(u,v),union(w,v))
| member(skf2(union(w,v),union(u,v)),u)
| subset(x,union(w,v)) ),
inference(res,[status(thm),theory(equality)],[72,36]),
[iquote('0:Res:72.2,36.0')] ).
cnf(430,plain,
( subset(union(u,v),u)
| member(skf2(u,union(u,v)),v) ),
inference(con,[status(thm)],[418]),
[iquote('0:Con:418.2')] ).
cnf(431,plain,
( subset(union(u,v),v)
| member(skf2(v,union(u,v)),u) ),
inference(con,[status(thm)],[425]),
[iquote('0:Con:425.2')] ).
cnf(432,plain,
( subset(union(u,v),union(w,v))
| member(skf2(union(w,v),union(u,v)),u) ),
inference(con,[status(thm)],[429]),
[iquote('0:Con:429.2')] ).
cnf(797,plain,
( subset(union(u,skc4),u)
| member(skf2(u,union(u,skc4)),skc3) ),
inference(res,[status(thm),theory(equality)],[430,3]),
[iquote('0:Res:430.1,3.0')] ).
cnf(1049,plain,
( subset(union(skc3,skc4),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[797,11]),
[iquote('0:Res:797.1,11.0')] ).
cnf(1054,plain,
subset(union(skc3,skc4),skc3),
inference(con,[status(thm)],[1049]),
[iquote('0:Con:1049.1')] ).
cnf(1084,plain,
equal(union(skc4,skc3),skc3),
inference(res,[status(thm),theory(equality)],[1054,250]),
[iquote('0:Res:1054.0,250.0')] ).
cnf(1091,plain,
equal(union(skc3,skc4),skc3),
inference(rew,[status(thm),theory(equality)],[7,1084]),
[iquote('0:Rew:7.0,1084.0')] ).
cnf(1167,plain,
( subset(union(skc5,u),u)
| member(skf2(u,union(skc5,u)),skc3) ),
inference(res,[status(thm),theory(equality)],[431,4]),
[iquote('0:Res:431.1,4.0')] ).
cnf(1213,plain,
( ~ member(skf2(union(u,skc5),v),skc3)
| member(skf2(union(u,skc5),v),skc4)
| subset(w,union(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[12,36]),
[iquote('0:Res:12.1,36.0')] ).
cnf(1635,plain,
( subset(union(skc5,skc3),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1167,11]),
[iquote('0:Res:1167.1,11.0')] ).
cnf(1640,plain,
subset(union(skc5,skc3),skc3),
inference(con,[status(thm)],[1635]),
[iquote('0:Con:1635.1')] ).
cnf(1641,plain,
subset(union(skc3,skc5),skc3),
inference(rew,[status(thm),theory(equality)],[7,1640]),
[iquote('0:Rew:7.0,1640.0')] ).
cnf(1689,plain,
( subset(union(u,skc4),union(skc3,skc4))
| member(skf2(skc3,union(u,skc4)),u) ),
inference(spr,[status(thm),theory(equality)],[1091,432]),
[iquote('0:SpR:1091.0,432.1')] ).
cnf(1730,plain,
( subset(union(u,skc4),skc3)
| member(skf2(skc3,union(u,skc4)),u) ),
inference(rew,[status(thm),theory(equality)],[1091,1689]),
[iquote('0:Rew:1091.0,1689.0')] ).
cnf(1742,plain,
equal(union(skc5,skc3),skc3),
inference(res,[status(thm),theory(equality)],[1641,250]),
[iquote('0:Res:1641.0,250.0')] ).
cnf(1749,plain,
equal(union(skc3,skc5),skc3),
inference(rew,[status(thm),theory(equality)],[7,1742]),
[iquote('0:Rew:7.0,1742.0')] ).
cnf(1790,plain,
( ~ member(skf2(skc3,u),skc5)
| subset(v,union(skc5,skc3)) ),
inference(spl,[status(thm),theory(equality)],[1749,236]),
[iquote('0:SpL:1749.0,236.0')] ).
cnf(1813,plain,
( ~ member(skf2(skc3,u),skc5)
| subset(v,skc3) ),
inference(rew,[status(thm),theory(equality)],[1749,1790,7]),
[iquote('0:Rew:1749.0,1790.1,7.0,1790.1')] ).
cnf(3708,plain,
( subset(union(skc5,skc4),skc3)
| subset(u,skc3) ),
inference(res,[status(thm),theory(equality)],[1730,1813]),
[iquote('0:Res:1730.1,1813.0')] ).
cnf(3712,plain,
subset(union(skc5,skc4),skc3),
inference(con,[status(thm)],[3708]),
[iquote('0:Con:3708.1')] ).
cnf(3713,plain,
subset(union(skc4,skc5),skc3),
inference(rew,[status(thm),theory(equality)],[7,3712]),
[iquote('0:Rew:7.0,3712.0')] ).
cnf(3714,plain,
~ subset(skc3,union(skc4,skc5)),
inference(mrr,[status(thm)],[20,3713]),
[iquote('0:MRR:20.1,3713.0')] ).
cnf(8141,plain,
( subset(skc3,union(u,skc5))
| member(skf2(union(u,skc5),skc3),skc4)
| subset(v,union(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[8,1213]),
[iquote('0:Res:8.1,1213.0')] ).
cnf(8165,plain,
( subset(skc3,union(u,skc5))
| member(skf2(union(u,skc5),skc3),skc4) ),
inference(con,[status(thm)],[8141]),
[iquote('0:Con:8141.2')] ).
cnf(14731,plain,
( subset(skc3,union(skc4,skc5))
| subset(u,union(skc4,skc5)) ),
inference(res,[status(thm),theory(equality)],[8165,37]),
[iquote('0:Res:8165.1,37.0')] ).
cnf(14739,plain,
subset(skc3,union(skc4,skc5)),
inference(con,[status(thm)],[14731]),
[iquote('0:Con:14731.1')] ).
cnf(14740,plain,
$false,
inference(mrr,[status(thm)],[14739,3714]),
[iquote('0:MRR:14739.0,3714.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 02:12:17 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.95/4.13
% 3.95/4.13 SPASS V 3.9
% 3.95/4.13 SPASS beiseite: Proof found.
% 3.95/4.13 % SZS status Theorem
% 3.95/4.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/4.13 SPASS derived 11946 clauses, backtracked 421 clauses, performed 7 splits and kept 3395 clauses.
% 3.95/4.13 SPASS allocated 94592 KBytes.
% 3.95/4.13 SPASS spent 0:00:03.71 on the problem.
% 3.95/4.13 0:00:00.03 for the input.
% 3.95/4.13 0:00:00.03 for the FLOTTER CNF translation.
% 3.95/4.13 0:00:00.14 for inferences.
% 3.95/4.13 0:00:00.05 for the backtracking.
% 3.95/4.13 0:00:03.41 for the reduction.
% 3.95/4.13
% 3.95/4.13
% 3.95/4.13 Here is a proof with depth 7, length 51 :
% 3.95/4.13 % SZS output start Refutation
% See solution above
% 3.95/4.13 Formulae used in the proof : prove_th18 commutativity_of_union subset_defn union_defn equal_defn
% 3.95/4.13
%------------------------------------------------------------------------------