%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET042-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 05:23:02 EDT 2022
% Result : Unsatisfiable 29.82s 30.04s
% Output : Refutation 29.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 7 unt; 0 nHn; 20 RR)
% Number of literals : 48 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 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(5,axiom,
( ~ little_set(u)
| ~ little_set(v)
| equal(first(ordered_pair(v,u)),v) ),
file('SET042-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ little_set(u)
| ~ little_set(v)
| equal(second(ordered_pair(v,u)),u) ),
file('SET042-3.p',unknown),
[] ).
cnf(10,axiom,
little_set(ordered_pair(u,v)),
file('SET042-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ ordered_pair_predicate(u)
| little_set(u) ),
file('SET042-3.p',unknown),
[] ).
cnf(27,axiom,
member(a,set_a),
file('SET042-3.p',unknown),
[] ).
cnf(28,axiom,
member(b,set_b),
file('SET042-3.p',unknown),
[] ).
cnf(29,axiom,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
file('SET042-3.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(u,v)
| little_set(u) ),
file('SET042-3.p',unknown),
[] ).
cnf(43,axiom,
( ~ little_set(u)
| ~ little_set(v)
| ~ equal(w,ordered_pair(v,u))
| ordered_pair_predicate(w) ),
file('SET042-3.p',unknown),
[] ).
cnf(70,axiom,
( ~ little_set(u)
| ~ ordered_pair_predicate(u)
| ~ member(first(u),v)
| ~ member(second(u),w)
| member(u,cross_product(v,w)) ),
file('SET042-3.p',unknown),
[] ).
cnf(174,plain,
( ~ ordered_pair_predicate(u)
| ~ member(second(u),v)
| ~ member(first(u),w)
| member(u,cross_product(w,v)) ),
inference(mrr,[status(thm)],[70,11]),
[iquote('0:MRR:70.0,11.1')] ).
cnf(190,plain,
little_set(b),
inference(res,[status(thm),theory(equality)],[28,30]),
[iquote('0:Res:28.0,30.0')] ).
cnf(191,plain,
little_set(a),
inference(res,[status(thm),theory(equality)],[27,30]),
[iquote('0:Res:27.0,30.0')] ).
cnf(4932,plain,
( ~ little_set(u)
| ~ little_set(v)
| ordered_pair_predicate(ordered_pair(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[43]),
[iquote('0:EqR:43.2')] ).
cnf(9735,plain,
( ~ ordered_pair_predicate(ordered_pair(a,b))
| ~ member(second(ordered_pair(a,b)),set_b)
| ~ member(first(ordered_pair(a,b)),set_a) ),
inference(res,[status(thm),theory(equality)],[174,29]),
[iquote('0:Res:174.3,29.0')] ).
cnf(24361,plain,
( ~ member(second(ordered_pair(a,b)),set_b)
| ~ member(first(ordered_pair(a,b)),set_a) ),
inference(ssi,[status(thm)],[9735,4932,191,190,10]),
[iquote('0:SSi:9735.0,4932.0,191.0,190.0,10.0,191.0,190.2')] ).
cnf(51830,plain,
( ~ little_set(b)
| ~ little_set(a)
| ~ member(b,set_b)
| ~ member(first(ordered_pair(a,b)),set_a) ),
inference(spl,[status(thm),theory(equality)],[6,24361]),
[iquote('0:SpL:6.2,24361.0')] ).
cnf(51879,plain,
( ~ little_set(b)
| ~ little_set(a)
| ~ member(b,set_b)
| ~ member(a,set_a) ),
inference(rew,[status(thm),theory(equality)],[5,51830]),
[iquote('0:Rew:5.2,51830.3')] ).
cnf(51880,plain,
( ~ member(b,set_b)
| ~ member(a,set_a) ),
inference(ssi,[status(thm)],[51879,191,190]),
[iquote('0:SSi:51879.1,51879.0,191.0,190.0')] ).
cnf(51881,plain,
$false,
inference(mrr,[status(thm)],[51880,28,27]),
[iquote('0:MRR:51880.0,51880.1,28.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET042-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n009.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 : Sun Jul 10 06:35:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.82/30.04
% 29.82/30.04 SPASS V 3.9
% 29.82/30.04 SPASS beiseite: Proof found.
% 29.82/30.04 % SZS status Theorem
% 29.82/30.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.82/30.04 SPASS derived 41810 clauses, backtracked 10441 clauses, performed 30 splits and kept 26273 clauses.
% 29.82/30.04 SPASS allocated 113610 KBytes.
% 29.82/30.04 SPASS spent 0:0:28.99 on the problem.
% 29.82/30.04 0:00:00.04 for the input.
% 29.82/30.04 0:00:00.00 for the FLOTTER CNF translation.
% 29.82/30.04 0:00:00.50 for inferences.
% 29.82/30.04 0:00:01.74 for the backtracking.
% 29.82/30.04 0:0:26.22 for the reduction.
% 29.82/30.04
% 29.82/30.04
% 29.82/30.04 Here is a proof with depth 2, length 20 :
% 29.82/30.04 % SZS output start Refutation
% See solution above
% 29.82/30.04 Formulae used in the proof : property_of_first property_of_second ordered_pairs_are_small1 ordered_pairs_are_small2 member_of_set_a member_of_set_b prove_ordered_pair_is_in_cross_product a2 ordered_pair_predicate4 cross_product4
% 29.82/30.04
%------------------------------------------------------------------------------