%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM066-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 : Mon Jul 18 14:23:56 EDT 2022
% Result : Unsatisfiable 21.75s 21.95s
% Output : Refutation 21.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 12 unt; 0 nHn; 26 RR)
% Number of literals : 52 ( 0 equ; 33 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
well_ordering(element_relation,y__dfg),
file('NUM066-1.p',unknown),
[] ).
cnf(2,axiom,
subclass(u__dfg,y__dfg),
file('NUM066-1.p',unknown),
[] ).
cnf(3,axiom,
member(v__dfg,u__dfg),
file('NUM066-1.p',unknown),
[] ).
cnf(4,axiom,
member(v__dfg,least(element_relation,u__dfg)),
file('NUM066-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('NUM066-1.p',unknown),
[] ).
cnf(8,axiom,
subclass(u,universal_class),
file('NUM066-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ member(u,v)
| ~ member(w,x)
| member(ordered_pair(w,u),cross_product(x,v)) ),
file('NUM066-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(ordered_pair(u,v),cross_product(universal_class,universal_class))
| member(ordered_pair(u,v),element_relation) ),
file('NUM066-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| ~ well_ordering(x,w)
| member(least(x,v),v) ),
file('NUM066-1.p',unknown),
[] ).
cnf(131,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| ~ well_ordering(x,w)
| ~ member(ordered_pair(u,least(x,v)),x) ),
file('NUM066-1.p',unknown),
[] ).
cnf(172,plain,
( ~ well_ordering(u,v)
| ~ subclass(u__dfg,v)
| ~ member(ordered_pair(v__dfg,least(u,u__dfg)),u) ),
inference(res,[status(thm),theory(equality)],[3,131]),
[iquote('0:Res:3.0,131.2')] ).
cnf(173,plain,
( ~ well_ordering(u,v)
| ~ subclass(u__dfg,v)
| member(least(u,u__dfg),u__dfg) ),
inference(res,[status(thm),theory(equality)],[3,129]),
[iquote('0:Res:3.0,129.2')] ).
cnf(175,plain,
( ~ member(u,u__dfg)
| member(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.0')] ).
cnf(189,plain,
( ~ subclass(least(element_relation,u__dfg),u)
| member(v__dfg,u) ),
inference(res,[status(thm),theory(equality)],[4,5]),
[iquote('0:Res:4.0,5.1')] ).
cnf(198,plain,
( ~ subclass(u__dfg,y__dfg)
| ~ member(ordered_pair(v__dfg,least(element_relation,u__dfg)),element_relation) ),
inference(res,[status(thm),theory(equality)],[1,172]),
[iquote('0:Res:1.0,172.0')] ).
cnf(199,plain,
( ~ subclass(u__dfg,y__dfg)
| member(least(element_relation,u__dfg),u__dfg) ),
inference(res,[status(thm),theory(equality)],[1,173]),
[iquote('0:Res:1.0,173.0')] ).
cnf(226,plain,
member(least(element_relation,u__dfg),u__dfg),
inference(mrr,[status(thm)],[199,2]),
[iquote('0:MRR:199.0,2.0')] ).
cnf(227,plain,
~ member(ordered_pair(v__dfg,least(element_relation,u__dfg)),element_relation),
inference(mrr,[status(thm)],[198,2]),
[iquote('0:MRR:198.0,2.0')] ).
cnf(251,plain,
member(least(element_relation,u__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[226,175]),
[iquote('0:Res:226.0,175.0')] ).
cnf(880,plain,
member(v__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[8,189]),
[iquote('0:Res:8.0,189.0')] ).
cnf(2328,plain,
( ~ subclass(y__dfg,u)
| member(least(element_relation,u__dfg),u) ),
inference(res,[status(thm),theory(equality)],[251,5]),
[iquote('0:Res:251.0,5.0')] ).
cnf(3186,plain,
( ~ member(u,universal_class)
| ~ member(v,universal_class)
| ~ member(v,u)
| member(ordered_pair(v,u),element_relation) ),
inference(res,[status(thm),theory(equality)],[20,24]),
[iquote('0:Res:20.2,24.1')] ).
cnf(62808,plain,
( ~ member(least(element_relation,u__dfg),universal_class)
| ~ member(v__dfg,universal_class)
| ~ member(v__dfg,least(element_relation,u__dfg)) ),
inference(res,[status(thm),theory(equality)],[3186,227]),
[iquote('0:Res:3186.3,227.0')] ).
cnf(62811,plain,
~ member(least(element_relation,u__dfg),universal_class),
inference(mrr,[status(thm)],[62808,880,4]),
[iquote('0:MRR:62808.1,62808.2,880.0,4.0')] ).
cnf(62839,plain,
~ subclass(y__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[2328,62811]),
[iquote('0:Res:2328.1,62811.0')] ).
cnf(62843,plain,
$false,
inference(mrr,[status(thm)],[62839,8]),
[iquote('0:MRR:62839.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM066-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 : Wed Jul 6 17:56:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 21.75/21.95
% 21.75/21.95 SPASS V 3.9
% 21.75/21.95 SPASS beiseite: Proof found.
% 21.75/21.95 % SZS status Theorem
% 21.75/21.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.75/21.95 SPASS derived 55129 clauses, backtracked 6783 clauses, performed 50 splits and kept 25520 clauses.
% 21.75/21.95 SPASS allocated 114561 KBytes.
% 21.75/21.95 SPASS spent 0:0:21.22 on the problem.
% 21.75/21.95 0:00:00.04 for the input.
% 21.75/21.95 0:00:00.00 for the FLOTTER CNF translation.
% 21.75/21.95 0:00:00.60 for inferences.
% 21.75/21.95 0:00:02.22 for the backtracking.
% 21.75/21.95 0:0:17.74 for the reduction.
% 21.75/21.95
% 21.75/21.95
% 21.75/21.95 Here is a proof with depth 5, length 26 :
% 21.75/21.95 % SZS output start Refutation
% See solution above
% 21.75/21.95 Formulae used in the proof : prove_corollary_to_well_ordering_property1_1 prove_corollary_to_well_ordering_property1_2 prove_corollary_to_well_ordering_property1_3 prove_corollary_to_well_ordering_property1_4 subclass_members class_elements_are_sets cartesian_product3 element_relation3 well_ordering3 well_ordering5
% 21.75/21.95
%------------------------------------------------------------------------------