TSTP Solution File: SET199+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:24:58 EDT 2022
% Result : Theorem 0.67s 0.85s
% Output : Refutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 9 unt; 15 nHn; 41 RR)
% Number of literals : 89 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc3,skc5),
file('SET199+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc3,skc4),
file('SET199+3.p',unknown),
[] ).
cnf(4,axiom,
~ subset(skc3,intersection(skc5,skc4)),
file('SET199+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET199+3.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET199+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET199+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET199+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET199+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET199+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET199+3.p',unknown),
[] ).
cnf(14,axiom,
( equal(u,v)
| member(skf3(v,u),v)
| member(skf3(v,u),u) ),
file('SET199+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(skf3(u,v),u)
| ~ member(skf3(u,v),v)
| equal(v,u) ),
file('SET199+3.p',unknown),
[] ).
cnf(16,plain,
~ subset(skc3,intersection(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(18,plain,
( ~ member(u,skc3)
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(25,plain,
( ~ member(skf2(skc5,u),skc3)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.1,9.0')] ).
cnf(31,plain,
( subset(intersection(u,v),w)
| member(skf2(w,intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.1,8.0')] ).
cnf(41,plain,
( ~ subset(u,v)
| subset(u,w)
| member(skf2(w,u),v) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.1,10.0')] ).
cnf(61,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subset(intersection(v,w),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[13,10]),
[iquote('0:Res:13.2,10.0')] ).
cnf(62,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)],[13,9]),
[iquote('0:Res:13.2,9.0')] ).
cnf(79,plain,
( subset(intersection(u,intersection(v,w)),x)
| member(skf2(x,intersection(u,intersection(v,w))),v) ),
inference(res,[status(thm),theory(equality)],[31,7]),
[iquote('0:Res:31.1,7.0')] ).
cnf(98,plain,
( equal(intersection(u,v),w)
| member(skf3(w,intersection(u,v)),w)
| member(skf3(w,intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[14,7]),
[iquote('0:Res:14.2,7.0')] ).
cnf(383,plain,
( equal(intersection(u,v),u)
| member(skf3(u,intersection(u,v)),u) ),
inference(fac,[status(thm)],[98]),
[iquote('0:Fac:98.1,98.2')] ).
cnf(406,plain,
( ~ member(skf3(u,intersection(u,v)),intersection(u,v))
| equal(intersection(u,v),u)
| equal(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[383,15]),
[iquote('0:Res:383.1,15.0')] ).
cnf(407,plain,
( ~ member(skf3(u,intersection(u,v)),intersection(u,v))
| equal(intersection(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[406]),
[iquote('0:Obv:406.1')] ).
cnf(418,plain,
( ~ member(skf3(u,intersection(u,v)),u)
| ~ member(skf3(u,intersection(u,v)),v)
| equal(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[13,407]),
[iquote('0:Res:13.2,407.0')] ).
cnf(423,plain,
( ~ member(skf3(u,intersection(u,v)),v)
| equal(intersection(u,v),u) ),
inference(mrr,[status(thm)],[418,383]),
[iquote('0:MRR:418.0,383.1')] ).
cnf(455,plain,
( equal(intersection(u,u),u)
| equal(intersection(u,u),u) ),
inference(res,[status(thm),theory(equality)],[383,423]),
[iquote('0:Res:383.1,423.0')] ).
cnf(460,plain,
equal(intersection(u,u),u),
inference(obv,[status(thm),theory(equality)],[455]),
[iquote('0:Obv:455.0')] ).
cnf(559,plain,
( subset(intersection(u,intersection(skc3,v)),skc5)
| subset(w,skc5) ),
inference(res,[status(thm),theory(equality)],[79,25]),
[iquote('0:Res:79.1,25.0')] ).
cnf(566,plain,
subset(intersection(u,intersection(skc3,v)),skc5),
inference(con,[status(thm)],[559]),
[iquote('0:Con:559.1')] ).
cnf(575,plain,
( ~ member(u,v)
| ~ member(u,intersection(skc3,w))
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[566,61]),
[iquote('0:Res:566.0,61.2')] ).
cnf(576,plain,
( ~ member(u,intersection(skc3,v))
| member(u,skc5) ),
inference(con,[status(thm)],[575]),
[iquote('0:Con:575.0')] ).
cnf(587,plain,
( ~ subset(u,v)
| ~ member(skf2(intersection(v,w),u),w)
| subset(u,intersection(v,w))
| subset(x,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[41,62]),
[iquote('0:Res:41.2,62.0')] ).
cnf(592,plain,
( ~ subset(u,v)
| ~ member(skf2(intersection(v,w),u),w)
| subset(u,intersection(v,w)) ),
inference(con,[status(thm)],[587]),
[iquote('0:Con:587.3')] ).
cnf(656,plain,
( subset(intersection(skc3,u),v)
| member(skf2(v,intersection(skc3,u)),skc5) ),
inference(res,[status(thm),theory(equality)],[6,576]),
[iquote('0:Res:6.1,576.0')] ).
cnf(760,plain,
( subset(intersection(skc3,skc3),u)
| member(skf2(u,skc3),skc5) ),
inference(spr,[status(thm),theory(equality)],[460,656]),
[iquote('0:SpR:460.0,656.1')] ).
cnf(765,plain,
( subset(skc3,u)
| member(skf2(u,skc3),skc5) ),
inference(rew,[status(thm),theory(equality)],[460,760]),
[iquote('0:Rew:460.0,760.0')] ).
cnf(2364,plain,
( ~ subset(skc3,u)
| subset(skc3,intersection(u,skc5))
| subset(skc3,intersection(u,skc5)) ),
inference(res,[status(thm),theory(equality)],[765,592]),
[iquote('0:Res:765.1,592.1')] ).
cnf(2367,plain,
( ~ subset(skc3,u)
| subset(skc3,intersection(u,skc5)) ),
inference(obv,[status(thm),theory(equality)],[2364]),
[iquote('0:Obv:2364.1')] ).
cnf(2505,plain,
~ subset(skc3,skc4),
inference(res,[status(thm),theory(equality)],[2367,16]),
[iquote('0:Res:2367.1,16.0')] ).
cnf(2506,plain,
$false,
inference(mrr,[status(thm)],[2505,2]),
[iquote('0:MRR:2505.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 : Sun Jul 10 02:08:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.67/0.85
% 0.67/0.85 SPASS V 3.9
% 0.67/0.85 SPASS beiseite: Proof found.
% 0.67/0.85 % SZS status Theorem
% 0.67/0.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.85 SPASS derived 2135 clauses, backtracked 188 clauses, performed 3 splits and kept 986 clauses.
% 0.67/0.85 SPASS allocated 86934 KBytes.
% 0.67/0.85 SPASS spent 0:00:00.50 on the problem.
% 0.67/0.85 0:00:00.04 for the input.
% 0.67/0.85 0:00:00.03 for the FLOTTER CNF translation.
% 0.67/0.85 0:00:00.03 for inferences.
% 0.67/0.85 0:00:00.00 for the backtracking.
% 0.67/0.85 0:00:00.37 for the reduction.
% 0.67/0.85
% 0.67/0.85
% 0.67/0.85 Here is a proof with depth 8, length 41 :
% 0.67/0.85 % SZS output start Refutation
% See solution above
% 0.67/0.85 Formulae used in the proof : prove_intersection_of_subsets commutativity_of_intersection subset_defn intersection_defn equal_member_defn
% 0.67/0.85
%------------------------------------------------------------------------------