%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET022-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 05:22:43 EDT 2022
% Result : Unsatisfiable 0.70s 0.87s
% Output : Refutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 4 unt; 0 nHn; 16 RR)
% Number of literals : 34 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 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('SET022-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ little_set(u)
| ~ little_set(v)
| equal(second(ordered_pair(v,u)),u) ),
file('SET022-3.p',unknown),
[] ).
cnf(7,axiom,
ordered_pair_predicate(a),
file('SET022-3.p',unknown),
[] ).
cnf(8,axiom,
~ little_set(first(a)),
file('SET022-3.p',unknown),
[] ).
cnf(19,axiom,
( ~ ordered_pair_predicate(u)
| little_set(f2(u)) ),
file('SET022-3.p',unknown),
[] ).
cnf(20,axiom,
( ~ ordered_pair_predicate(u)
| little_set(f3(u)) ),
file('SET022-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ ordered_pair_predicate(u)
| equal(ordered_pair(f2(u),f3(u)),u) ),
file('SET022-3.p',unknown),
[] ).
cnf(1383,plain,
( ~ ordered_pair_predicate(u)
| ~ little_set(f3(u))
| ~ little_set(f2(u))
| equal(f3(u),second(u)) ),
inference(spr,[status(thm),theory(equality)],[21,6]),
[iquote('0:SpR:21.1,6.2')] ).
cnf(1390,plain,
( ~ ordered_pair_predicate(u)
| equal(f3(u),second(u)) ),
inference(ssi,[status(thm)],[1383,19,20]),
[iquote('0:SSi:1383.2,1383.1,19.1,20.1')] ).
cnf(1391,plain,
( ~ ordered_pair_predicate(u)
| little_set(second(u)) ),
inference(rew,[status(thm),theory(equality)],[1390,20]),
[iquote('0:Rew:1390.1,20.1')] ).
cnf(1392,plain,
( ~ ordered_pair_predicate(u)
| equal(ordered_pair(f2(u),second(u)),u) ),
inference(rew,[status(thm),theory(equality)],[1390,21]),
[iquote('0:Rew:1390.1,21.1')] ).
cnf(2762,plain,
( ~ ordered_pair_predicate(u)
| ~ little_set(second(u))
| ~ little_set(f2(u))
| equal(f2(u),first(u)) ),
inference(spr,[status(thm),theory(equality)],[1392,5]),
[iquote('0:SpR:1392.1,5.2')] ).
cnf(2771,plain,
( ~ ordered_pair_predicate(u)
| equal(f2(u),first(u)) ),
inference(ssi,[status(thm)],[2762,19,1391]),
[iquote('0:SSi:2762.2,2762.1,19.1,1391.1')] ).
cnf(2772,plain,
( ~ ordered_pair_predicate(u)
| little_set(first(u)) ),
inference(rew,[status(thm),theory(equality)],[2771,19]),
[iquote('0:Rew:2771.1,19.1')] ).
cnf(2781,plain,
~ ordered_pair_predicate(a),
inference(res,[status(thm),theory(equality)],[2772,8]),
[iquote('0:Res:2772.1,8.0')] ).
cnf(2783,plain,
$false,
inference(ssi,[status(thm)],[2781,7]),
[iquote('0:SSi:2781.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET022-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 21:28:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/0.87
% 0.70/0.87 SPASS V 3.9
% 0.70/0.87 SPASS beiseite: Proof found.
% 0.70/0.87 % SZS status Theorem
% 0.70/0.87 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.87 SPASS derived 2197 clauses, backtracked 641 clauses, performed 9 splits and kept 1957 clauses.
% 0.70/0.87 SPASS allocated 78354 KBytes.
% 0.70/0.87 SPASS spent 0:00:00.51 on the problem.
% 0.70/0.87 0:00:00.04 for the input.
% 0.70/0.87 0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.87 0:00:00.02 for inferences.
% 0.70/0.87 0:00:00.01 for the backtracking.
% 0.70/0.87 0:00:00.39 for the reduction.
% 0.70/0.87
% 0.70/0.87
% 0.70/0.87 Here is a proof with depth 1, length 16 :
% 0.70/0.87 % SZS output start Refutation
% See solution above
% 0.70/0.87 Formulae used in the proof : property_of_first property_of_second an_ordered_pair_predicate prove_first_component_is_small ordered_pair_predicate1 ordered_pair_predicate2 ordered_pair_predicate3
% 0.70/0.87
%------------------------------------------------------------------------------