TSTP Solution File: SET787-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:28:40 EDT 2022
% Result : Unsatisfiable 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 15 unt; 3 nHn; 22 RR)
% Number of literals : 30 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(u,union(v))
| member(u,unionE_sk1(u,v)) ),
file('SET787-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,union(v))
| member(unionE_sk1(u,v),v) ),
file('SET787-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,cons(v,w))
| member(u,w)
| equal(u,v) ),
file('SET787-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(u,v)
| member(u,un(v,w)) ),
file('SET787-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(u,v)
| member(u,un(w,v)) ),
file('SET787-1.p',unknown),
[] ).
cnf(8,axiom,
~ member(u,eptset),
file('SET787-1.p',unknown),
[] ).
cnf(13,axiom,
member(sk2,union(cons(a,cons(b,eptset)))),
file('SET787-1.p',unknown),
[] ).
cnf(14,axiom,
~ member(sk2,un(a,b)),
file('SET787-1.p',unknown),
[] ).
cnf(15,plain,
~ member(sk2,b),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.1,14.0')] ).
cnf(16,plain,
~ member(sk2,a),
inference(res,[status(thm),theory(equality)],[6,14]),
[iquote('0:Res:6.1,14.0')] ).
cnf(20,plain,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.0')] ).
cnf(21,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(res,[status(thm),theory(equality)],[13,2]),
[iquote('0:Res:13.0,2.0')] ).
cnf(85,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),a) ),
inference(res,[status(thm),theory(equality)],[21,5]),
[iquote('0:Res:21.0,5.0')] ).
cnf(745,plain,
equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),a),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(746,plain,
member(sk2,a),
inference(rew,[status(thm),theory(equality)],[745,20]),
[iquote('1:Rew:745.0,20.0')] ).
cnf(748,plain,
$false,
inference(mrr,[status(thm)],[746,16]),
[iquote('1:MRR:746.0,16.0')] ).
cnf(749,plain,
~ equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),a),
inference(spt,[spt(split,[position(sa)])],[748,745]),
[iquote('1:Spt:748.0,85.1,745.0')] ).
cnf(750,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:748.0,85.0')] ).
cnf(751,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),b) ),
inference(res,[status(thm),theory(equality)],[750,5]),
[iquote('1:Res:750.0,5.0')] ).
cnf(752,plain,
equal(unionE_sk1(sk2,cons(a,cons(b,eptset))),b),
inference(mrr,[status(thm)],[751,8]),
[iquote('1:MRR:751.0,8.0')] ).
cnf(754,plain,
member(sk2,b),
inference(rew,[status(thm),theory(equality)],[752,20]),
[iquote('1:Rew:752.0,20.0')] ).
cnf(757,plain,
$false,
inference(mrr,[status(thm)],[754,15]),
[iquote('1:MRR:754.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.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 02:57:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.54
% 0.21/0.54 SPASS V 3.9
% 0.21/0.54 SPASS beiseite: Proof found.
% 0.21/0.54 % SZS status Theorem
% 0.21/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 SPASS derived 665 clauses, backtracked 4 clauses, performed 1 splits and kept 548 clauses.
% 0.21/0.54 SPASS allocated 64110 KBytes.
% 0.21/0.54 SPASS spent 0:00:00.18 on the problem.
% 0.21/0.54 0:00:00.04 for the input.
% 0.21/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.54 0:00:00.01 for inferences.
% 0.21/0.54 0:00:00.00 for the backtracking.
% 0.21/0.54 0:00:00.09 for the reduction.
% 0.21/0.54
% 0.21/0.54
% 0.21/0.54 Here is a proof with depth 4, length 22 :
% 0.21/0.54 % SZS output start Refutation
% See solution above
% 0.21/0.55 Formulae used in the proof : clause119 clause120 clause112 unI1 unI2 clause158 un_eq_Union_2_c1 un_eq_Union_2_c2
% 0.21/0.55
%------------------------------------------------------------------------------