%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET121-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:24:19 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 5 unt; 3 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 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(4,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(v,universal_class) ),
file('SET121-7.p',unknown),
[] ).
cnf(69,axiom,
( member(ordered_pair(first(u),second(u)),cross_product(universal_class,universal_class))
| equal(first(u),u) ),
file('SET121-7.p',unknown),
[] ).
cnf(71,axiom,
( equal(first(u),u)
| equal(ordered_pair(first(u),second(u)),u) ),
file('SET121-7.p',unknown),
[] ).
cnf(77,axiom,
~ member(y__dfg,universal_class),
file('SET121-7.p',unknown),
[] ).
cnf(78,axiom,
~ equal(first(ordered_pair(x__dfg,y__dfg)),ordered_pair(x__dfg,y__dfg)),
file('SET121-7.p',unknown),
[] ).
cnf(174,plain,
( member(u,cross_product(universal_class,universal_class))
| equal(first(u),u) ),
inference(rew,[status(thm),theory(equality)],[71,69]),
[iquote('0:Rew:71.0,69.0')] ).
cnf(193,plain,
~ member(ordered_pair(u,y__dfg),cross_product(v,w)),
inference(res,[status(thm),theory(equality)],[4,77]),
[iquote('0:Res:4.1,77.0')] ).
cnf(201,plain,
member(ordered_pair(x__dfg,y__dfg),cross_product(universal_class,universal_class)),
inference(res,[status(thm),theory(equality)],[174,78]),
[iquote('0:Res:174.1,78.0')] ).
cnf(232,plain,
$false,
inference(unc,[status(thm)],[193,201]),
[iquote('0:UnC:193.0,201.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET121-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 10:47:12 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 28 clauses, backtracked 0 clauses, performed 0 splits and kept 172 clauses.
% 0.19/0.45 SPASS allocated 75845 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.01 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 1, length 9 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : corollary_2_to_cartesian_product unique_1st_and_2nd_in_pair_of_non_sets1 unique_1st_and_2nd_in_pair_of_non_sets3 prove_corollary_1_to_OP_determines_components2_1 prove_corollary_1_to_OP_determines_components2_2
% 0.19/0.45
%------------------------------------------------------------------------------