%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET013-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 05:22:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 13 unt; 2 nHn; 28 RR)
% Number of literals : 48 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 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(3,axiom,
( equal(u,v)
| member(f1(u,v),v)
| member(f1(u,v),u) ),
file('SET013-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(f1(u,v),v)
| ~ member(f1(u,v),u)
| equal(u,v) ),
file('SET013-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET013-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET013-4.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET013-4.p',unknown),
[] ).
cnf(10,axiom,
equal(intersection(as,bs),cs),
file('SET013-4.p',unknown),
[] ).
cnf(11,axiom,
equal(intersection(bs,as),ds),
file('SET013-4.p',unknown),
[] ).
cnf(12,axiom,
~ equal(ds,cs),
file('SET013-4.p',unknown),
[] ).
cnf(16,plain,
( ~ member(f1(cs,ds),ds)
| ~ member(f1(cs,ds),cs) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.2,12.0')] ).
cnf(17,plain,
( member(f1(cs,ds),ds)
| member(f1(cs,ds),cs) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.2,12.0')] ).
cnf(22,plain,
( ~ member(u,ds)
| member(u,as) ),
inference(spl,[status(thm),theory(equality)],[11,6]),
[iquote('0:SpL:11.0,6.0')] ).
cnf(23,plain,
( ~ member(u,cs)
| member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpL:10.0,6.0')] ).
cnf(24,plain,
( ~ member(u,ds)
| member(u,bs) ),
inference(spl,[status(thm),theory(equality)],[11,5]),
[iquote('0:SpL:11.0,5.0')] ).
cnf(25,plain,
( ~ member(u,cs)
| member(u,as) ),
inference(spl,[status(thm),theory(equality)],[10,5]),
[iquote('0:SpL:10.0,5.0')] ).
cnf(26,plain,
( ~ member(u,as)
| ~ member(u,bs)
| member(u,ds) ),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.2')] ).
cnf(27,plain,
( ~ member(u,bs)
| ~ member(u,as)
| member(u,cs) ),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.2')] ).
cnf(32,plain,
member(f1(cs,ds),ds),
inference(spt,[spt(split,[position(s1)])],[17]),
[iquote('1:Spt:17.0')] ).
cnf(33,plain,
~ member(f1(cs,ds),cs),
inference(mrr,[status(thm)],[16,32]),
[iquote('1:MRR:16.0,32.0')] ).
cnf(35,plain,
member(f1(cs,ds),bs),
inference(res,[status(thm),theory(equality)],[32,24]),
[iquote('1:Res:32.0,24.0')] ).
cnf(36,plain,
member(f1(cs,ds),as),
inference(res,[status(thm),theory(equality)],[32,22]),
[iquote('1:Res:32.0,22.0')] ).
cnf(227,plain,
( ~ member(f1(cs,ds),bs)
| ~ member(f1(cs,ds),as) ),
inference(res,[status(thm),theory(equality)],[27,33]),
[iquote('1:Res:27.2,33.0')] ).
cnf(228,plain,
$false,
inference(mrr,[status(thm)],[227,35,36]),
[iquote('1:MRR:227.0,227.1,35.0,36.0')] ).
cnf(229,plain,
~ member(f1(cs,ds),ds),
inference(spt,[spt(split,[position(sa)])],[228,32]),
[iquote('1:Spt:228.0,17.0,32.0')] ).
cnf(230,plain,
member(f1(cs,ds),cs),
inference(spt,[spt(split,[position(s2)])],[17]),
[iquote('1:Spt:228.0,17.1')] ).
cnf(232,plain,
member(f1(cs,ds),as),
inference(res,[status(thm),theory(equality)],[230,25]),
[iquote('1:Res:230.0,25.0')] ).
cnf(233,plain,
member(f1(cs,ds),bs),
inference(res,[status(thm),theory(equality)],[230,23]),
[iquote('1:Res:230.0,23.0')] ).
cnf(385,plain,
( ~ member(f1(cs,ds),as)
| ~ member(f1(cs,ds),bs) ),
inference(res,[status(thm),theory(equality)],[26,229]),
[iquote('1:Res:26.2,229.0')] ).
cnf(387,plain,
$false,
inference(mrr,[status(thm)],[385,232,233]),
[iquote('1:MRR:385.0,385.1,232.0,233.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET013-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 05:37:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 307 clauses, backtracked 115 clauses, performed 7 splits and kept 241 clauses.
% 0.19/0.44 SPASS allocated 75795 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.02 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 3, length 28 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : extensionality2 extensionality3 intersection1 intersection2 intersection3 intersection_of_a_and_b_is_c intersection_of_b_and_a_is_d prove_c_equals_d
% 0.19/0.44
%------------------------------------------------------------------------------