%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 05:25:00 EDT 2022
% Result : Theorem 5.73s 5.92s
% Output : Refutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 9 unt; 7 nHn; 26 RR)
% Number of literals : 51 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
subset(skc7,skc6),
file('SET201+3.p',unknown),
[] ).
cnf(2,axiom,
subset(skc4,skc5),
file('SET201+3.p',unknown),
[] ).
cnf(4,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET201+3.p',unknown),
[] ).
cnf(5,axiom,
~ subset(intersection(skc7,skc4),intersection(skc6,skc5)),
file('SET201+3.p',unknown),
[] ).
cnf(6,axiom,
( subset(u,v)
| member(skf2(v,u),u) ),
file('SET201+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET201+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(skf2(u,v),u)
| subset(w,u) ),
file('SET201+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,v)
| ~ subset(v,w)
| member(u,w) ),
file('SET201+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(v,w)) ),
file('SET201+3.p',unknown),
[] ).
cnf(16,plain,
~ subset(intersection(skc4,skc7),intersection(skc5,skc6)),
inference(rew,[status(thm),theory(equality)],[4,5]),
[iquote('0:Rew:4.0,5.0,4.0,5.0')] ).
cnf(17,plain,
( ~ member(u,skc4)
| member(u,skc5) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(18,plain,
( ~ member(u,skc7)
| member(u,skc6) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(26,plain,
( ~ member(skf2(skc5,u),skc4)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[17,9]),
[iquote('0:Res:17.1,9.0')] ).
cnf(35,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(40,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(58,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(85,plain,
( subset(intersection(u,skc7),v)
| member(skf2(v,intersection(u,skc7)),skc6) ),
inference(res,[status(thm),theory(equality)],[35,18]),
[iquote('0:Res:35.1,18.0')] ).
cnf(90,plain,
( subset(intersection(u,skc4),skc5)
| subset(v,skc5) ),
inference(res,[status(thm),theory(equality)],[35,26]),
[iquote('0:Res:35.1,26.0')] ).
cnf(92,plain,
subset(intersection(u,skc4),skc5),
inference(con,[status(thm)],[90]),
[iquote('0:Con:90.1')] ).
cnf(94,plain,
subset(intersection(skc4,u),skc5),
inference(spr,[status(thm),theory(equality)],[4,92]),
[iquote('0:SpR:4.0,92.0')] ).
cnf(512,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)],[40,58]),
[iquote('0:Res:40.2,58.0')] ).
cnf(524,plain,
( ~ subset(u,v)
| ~ member(skf2(intersection(v,w),u),w)
| subset(u,intersection(v,w)) ),
inference(con,[status(thm)],[512]),
[iquote('0:Con:512.3')] ).
cnf(1974,plain,
( ~ subset(intersection(u,skc7),v)
| subset(intersection(u,skc7),intersection(v,skc6))
| subset(intersection(u,skc7),intersection(v,skc6)) ),
inference(res,[status(thm),theory(equality)],[85,524]),
[iquote('0:Res:85.1,524.1')] ).
cnf(1986,plain,
( ~ subset(intersection(u,skc7),v)
| subset(intersection(u,skc7),intersection(v,skc6)) ),
inference(obv,[status(thm),theory(equality)],[1974]),
[iquote('0:Obv:1974.1')] ).
cnf(9632,plain,
~ subset(intersection(skc4,skc7),skc5),
inference(res,[status(thm),theory(equality)],[1986,16]),
[iquote('0:Res:1986.1,16.0')] ).
cnf(9633,plain,
$false,
inference(mrr,[status(thm)],[9632,94]),
[iquote('0:MRR:9632.0,94.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET201+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 18:46:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 5.73/5.92
% 5.73/5.92 SPASS V 3.9
% 5.73/5.92 SPASS beiseite: Proof found.
% 5.73/5.92 % SZS status Theorem
% 5.73/5.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.73/5.92 SPASS derived 7925 clauses, backtracked 1120 clauses, performed 4 splits and kept 4271 clauses.
% 5.73/5.92 SPASS allocated 92318 KBytes.
% 5.73/5.92 SPASS spent 0:00:05.52 on the problem.
% 5.73/5.92 0:00:00.03 for the input.
% 5.73/5.92 0:00:00.03 for the FLOTTER CNF translation.
% 5.73/5.92 0:00:00.10 for inferences.
% 5.73/5.92 0:00:00.05 for the backtracking.
% 5.73/5.92 0:00:05.27 for the reduction.
% 5.73/5.92
% 5.73/5.92
% 5.73/5.92 Here is a proof with depth 4, length 26 :
% 5.73/5.92 % SZS output start Refutation
% See solution above
% 5.73/5.92 Formulae used in the proof : prove_th41 commutativity_of_intersection subset_defn intersection_defn
% 5.73/5.92
%------------------------------------------------------------------------------