TSTP Solution File: SET628+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 05:27:39 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 27 ( 13 unt; 8 nHn; 27 RR)
% Number of literals : 45 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(u,empty_set),
file('SET628+3.p',unknown),
[] ).
cnf(2,axiom,
( intersect(skc1,skc1)
| not_equal(skc1,empty_set) ),
file('SET628+3.p',unknown),
[] ).
cnf(3,axiom,
( not_equal(u,v)
| equal(u,v) ),
file('SET628+3.p',unknown),
[] ).
cnf(4,axiom,
( empty(u)
| member(skf5(u),u) ),
file('SET628+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ empty(u)
| ~ member(v,u) ),
file('SET628+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ intersect(skc1,skc1)
| ~ not_equal(skc1,empty_set) ),
file('SET628+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,v)
| ~ not_equal(u,v) ),
file('SET628+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ intersect(u,v)
| member(skf3(v,u),u) ),
file('SET628+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ member(u,w)
| intersect(w,v) ),
file('SET628+3.p',unknown),
[] ).
cnf(14,axiom,
( equal(u,v)
| member(skf4(v,u),v)
| member(skf4(v,u),u) ),
file('SET628+3.p',unknown),
[] ).
cnf(16,plain,
intersect(skc1,skc1),
inference(spt,[spt(split,[position(s1)])],[2]),
[iquote('1:Spt:2.0')] ).
cnf(17,plain,
~ not_equal(skc1,empty_set),
inference(mrr,[status(thm)],[7,16]),
[iquote('1:MRR:7.0,16.0')] ).
cnf(19,plain,
equal(skc1,empty_set),
inference(res,[status(thm),theory(equality)],[3,17]),
[iquote('1:Res:3.0,17.0')] ).
cnf(20,plain,
intersect(empty_set,empty_set),
inference(rew,[status(thm),theory(equality)],[19,16]),
[iquote('1:Rew:19.0,16.0')] ).
cnf(27,plain,
~ intersect(empty_set,u),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.1,1.0')] ).
cnf(29,plain,
$false,
inference(unc,[status(thm)],[27,20]),
[iquote('1:UnC:27.0,20.0')] ).
cnf(30,plain,
~ intersect(skc1,skc1),
inference(spt,[spt(split,[position(sa)])],[29,16]),
[iquote('1:Spt:29.0,2.0,16.0')] ).
cnf(31,plain,
not_equal(skc1,empty_set),
inference(spt,[spt(split,[position(s2)])],[2]),
[iquote('1:Spt:29.0,2.1')] ).
cnf(32,plain,
~ equal(skc1,empty_set),
inference(res,[status(thm),theory(equality)],[31,8]),
[iquote('1:Res:31.0,8.1')] ).
cnf(33,plain,
( ~ member(skf5(u),v)
| empty(u)
| intersect(v,u) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.1,11.0')] ).
cnf(36,plain,
( empty(u)
| empty(u)
| intersect(u,u) ),
inference(res,[status(thm),theory(equality)],[4,33]),
[iquote('0:Res:4.1,33.0')] ).
cnf(37,plain,
( empty(u)
| intersect(u,u) ),
inference(obv,[status(thm),theory(equality)],[36]),
[iquote('0:Obv:36.0')] ).
cnf(42,plain,
empty(skc1),
inference(res,[status(thm),theory(equality)],[37,30]),
[iquote('1:Res:37.1,30.0')] ).
cnf(47,plain,
( equal(u,empty_set)
| member(skf4(empty_set,u),u) ),
inference(res,[status(thm),theory(equality)],[14,1]),
[iquote('0:Res:14.1,1.0')] ).
cnf(54,plain,
( ~ empty(u)
| equal(u,empty_set) ),
inference(res,[status(thm),theory(equality)],[47,6]),
[iquote('0:Res:47.1,6.1')] ).
cnf(56,plain,
equal(skc1,empty_set),
inference(ems,[status(thm)],[54,42]),
[iquote('1:EmS:54.0,42.0')] ).
cnf(58,plain,
$false,
inference(mrr,[status(thm)],[56,32]),
[iquote('1:MRR:56.0,32.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 11 02:36:16 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.46
% 0.22/0.46 SPASS V 3.9
% 0.22/0.46 SPASS beiseite: Proof found.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 SPASS derived 38 clauses, backtracked 4 clauses, performed 1 splits and kept 41 clauses.
% 0.22/0.46 SPASS allocated 97794 KBytes.
% 0.22/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.22/0.46 0:00:00.04 for the input.
% 0.22/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.46 0:00:00.00 for inferences.
% 0.22/0.46 0:00:00.00 for the backtracking.
% 0.22/0.46 0:00:00.00 for the reduction.
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 Here is a proof with depth 4, length 27 :
% 0.22/0.46 % SZS output start Refutation
% See solution above
% 0.22/0.46 Formulae used in the proof : empty_set_defn prove_th110 not_equal_defn empty_defn intersect_defn equal_member_defn
% 0.22/0.46
%------------------------------------------------------------------------------