TSTP Solution File: SET002-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:22:18 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 6 unt; 6 nHn; 19 RR)
% Number of literals : 37 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
union(a,a,aUa),
file('SET002-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal_sets(aUa,a),
file('SET002-1.p',unknown),
[] ).
cnf(4,axiom,
( subset(u,v)
| member(member_of_1_not_of_2(u,v),u) ),
file('SET002-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(member_of_1_not_of_2(u,v),v)
| subset(u,v) ),
file('SET002-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(u,v)
| ~ subset(v,u)
| equal_sets(u,v) ),
file('SET002-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,v)
| ~ union(w,x,v)
| member(u,x)
| member(u,w) ),
file('SET002-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| ~ union(w,v,x)
| member(u,x) ),
file('SET002-1.p',unknown),
[] ).
cnf(15,plain,
( ~ subset(aUa,a)
| ~ subset(a,aUa) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.2,2.0')] ).
cnf(31,plain,
( ~ member(u,a)
| member(u,aUa) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.1')] ).
cnf(32,plain,
( subset(a,u)
| member(member_of_1_not_of_2(a,u),aUa) ),
inference(res,[status(thm),theory(equality)],[4,31]),
[iquote('0:Res:4.1,31.0')] ).
cnf(33,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(res,[status(thm),theory(equality)],[32,5]),
[iquote('0:Res:32.1,5.0')] ).
cnf(34,plain,
subset(a,aUa),
inference(obv,[status(thm),theory(equality)],[33]),
[iquote('0:Obv:33.0')] ).
cnf(35,plain,
~ subset(aUa,a),
inference(mrr,[status(thm)],[15,34]),
[iquote('0:MRR:15.1,34.0')] ).
cnf(42,plain,
( ~ member(u,aUa)
| member(u,a)
| member(u,a) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.1')] ).
cnf(43,plain,
( ~ member(u,aUa)
| member(u,a) ),
inference(obv,[status(thm),theory(equality)],[42]),
[iquote('0:Obv:42.1')] ).
cnf(44,plain,
( ~ member(member_of_1_not_of_2(u,a),aUa)
| subset(u,a) ),
inference(res,[status(thm),theory(equality)],[43,5]),
[iquote('0:Res:43.1,5.0')] ).
cnf(46,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(res,[status(thm),theory(equality)],[4,44]),
[iquote('0:Res:4.1,44.0')] ).
cnf(48,plain,
subset(aUa,a),
inference(obv,[status(thm),theory(equality)],[46]),
[iquote('0:Obv:46.0')] ).
cnf(49,plain,
$false,
inference(mrr,[status(thm)],[48,35]),
[iquote('0:MRR:48.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 : Mon Jul 11 10:07:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 28 clauses.
% 0.19/0.42 SPASS allocated 63108 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.00 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 19 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : a_union_a_is_aUa prove_a_equals_aUa subsets_axiom1 subsets_axiom2 subsets_are_set_equal_sets member_of_union_is_member_of_one_set member_of_set2_is_member_of_union
% 0.19/0.42
%------------------------------------------------------------------------------