%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET051-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:23:10 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 0 equ; 7 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(ordered_pair(x__dfg,y__dfg),cross_product(u__dfg,v__dfg)),
file('SET051-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(y__dfg,unordered_pair(x__dfg,y__dfg)),
file('SET051-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET051-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET051-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET051-6.p',unknown),
[] ).
cnf(17,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,x) ),
file('SET051-6.p',unknown),
[] ).
cnf(101,plain,
~ member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.1,2.0')] ).
cnf(106,plain,
member(y__dfg,v__dfg),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.0')] ).
cnf(306,plain,
( ~ subclass(v__dfg,u)
| member(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[106,3]),
[iquote('0:Res:106.0,3.0')] ).
cnf(329,plain,
member(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[6,306]),
[iquote('0:Res:6.0,306.0')] ).
cnf(333,plain,
$false,
inference(mrr,[status(thm)],[329,101]),
[iquote('0:MRR:329.0,101.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET051-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 16:07:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 200 clauses, backtracked 0 clauses, performed 0 splits and kept 241 clauses.
% 0.19/0.46 SPASS allocated 76037 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.46 0:00:00.04 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.01 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 3, length 11 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : prove_corollary_2_to_unordered_pair_1 prove_corollary_2_to_unordered_pair_2 subclass_members class_elements_are_sets unordered_pair3 cartesian_product2
% 0.19/0.46
%------------------------------------------------------------------------------