%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM095-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 14:24:05 EDT 2022
% Result : Unsatisfiable 58.03s 58.24s
% Output : Refutation 58.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of clauses : 65 ( 20 unt; 15 nHn; 65 RR)
% Number of literals : 122 ( 0 equ; 51 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
well_ordering(xr,y__dfg),
file('NUM095-1.p',unknown),
[] ).
cnf(2,axiom,
section(xr,w__dfg,y__dfg),
file('NUM095-1.p',unknown),
[] ).
cnf(3,axiom,
~ member(least(xr,intersection(complement(w__dfg),y__dfg)),complement(w__dfg)),
file('NUM095-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(w__dfg,y__dfg),
file('NUM095-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('NUM095-1.p',unknown),
[] ).
cnf(6,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('NUM095-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('NUM095-1.p',unknown),
[] ).
cnf(8,axiom,
subclass(u,universal_class),
file('NUM095-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('NUM095-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('NUM095-1.p',unknown),
[] ).
cnf(15,axiom,
member(unordered_pair(u,v),universal_class),
file('NUM095-1.p',unknown),
[] ).
cnf(17,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('NUM095-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ member(ordered_pair(u,v),cross_product(w,x))
| member(u,w) ),
file('NUM095-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('NUM095-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('NUM095-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('NUM095-1.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('NUM095-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('NUM095-1.p',unknown),
[] ).
cnf(66,axiom,
( ~ function(u)
| subclass(u,cross_product(universal_class,universal_class)) ),
file('NUM095-1.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('NUM095-1.p',unknown),
[] ).
cnf(71,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('NUM095-1.p',unknown),
[] ).
cnf(128,axiom,
( ~ subclass(u,v)
| ~ well_ordering(w,v)
| equal(u,null_class)
| member(least(w,u),u) ),
file('NUM095-1.p',unknown),
[] ).
cnf(135,axiom,
( ~ section(u,v,w)
| subclass(v,w) ),
file('NUM095-1.p',unknown),
[] ).
cnf(151,axiom,
( ~ member(u,recursion_equation_functions(v))
| function(v) ),
file('NUM095-1.p',unknown),
[] ).
cnf(167,plain,
( ~ subclass(u,y__dfg)
| equal(u,null_class)
| member(least(xr,u),u) ),
inference(res,[status(thm),theory(equality)],[1,128]),
[iquote('0:Res:1.0,128.0')] ).
cnf(171,plain,
( ~ subclass(w__dfg,y__dfg)
| ~ subclass(y__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[11,4]),
[iquote('0:Res:11.2,4.0')] ).
cnf(177,plain,
subclass(w__dfg,y__dfg),
inference(res,[status(thm),theory(equality)],[2,135]),
[iquote('0:Res:2.0,135.0')] ).
cnf(181,plain,
~ member(least(xr,intersection(complement(w__dfg),y__dfg)),intersection(complement(w__dfg),u)),
inference(res,[status(thm),theory(equality)],[25,3]),
[iquote('0:Res:25.1,3.0')] ).
cnf(186,plain,
~ subclass(y__dfg,w__dfg),
inference(mrr,[status(thm)],[171,177]),
[iquote('0:MRR:171.0,177.0')] ).
cnf(371,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[6,28]),
[iquote('0:Res:6.1,28.1')] ).
cnf(384,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[6,26]),
[iquote('0:Res:6.1,26.0')] ).
cnf(394,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[6,25]),
[iquote('0:Res:6.1,25.0')] ).
cnf(1036,plain,
member(ordered_pair(u,v),universal_class),
inference(spr,[status(thm),theory(equality)],[17,15]),
[iquote('0:SpR:17.0,15.0')] ).
cnf(1525,plain,
( ~ subclass(universal_class,u)
| member(ordered_pair(v,w),u) ),
inference(res,[status(thm),theory(equality)],[1036,5]),
[iquote('0:Res:1036.0,5.0')] ).
cnf(3610,plain,
( ~ subclass(universal_class,cross_product(u,v))
| member(w,u) ),
inference(res,[status(thm),theory(equality)],[1525,18]),
[iquote('0:Res:1525.1,18.0')] ).
cnf(3790,plain,
( ~ function(universal_class)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[66,3610]),
[iquote('0:Res:66.1,3610.0')] ).
cnf(4909,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[27,5]),
[iquote('0:Res:27.2,5.0')] ).
cnf(8836,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[384,7]),
[iquote('0:Res:384.1,7.0')] ).
cnf(8841,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[8836]),
[iquote('0:Obv:8836.0')] ).
cnf(9127,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[394,7]),
[iquote('0:Res:394.1,7.0')] ).
cnf(9132,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[9127]),
[iquote('0:Obv:9127.0')] ).
cnf(33998,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[8,4909]),
[iquote('0:Res:8.0,4909.2')] ).
cnf(34005,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[33998]),
[iquote('0:Con:33998.1')] ).
cnf(34138,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[6,34005]),
[iquote('0:Res:6.1,34005.0')] ).
cnf(35818,plain,
( subclass(complement(universal_class),u)
| subclass(complement(universal_class),u) ),
inference(res,[status(thm),theory(equality)],[34138,371]),
[iquote('0:Res:34138.1,371.0')] ).
cnf(35826,plain,
subclass(complement(universal_class),u),
inference(obv,[status(thm),theory(equality)],[35818]),
[iquote('0:Obv:35818.0')] ).
cnf(83916,plain,
( equal(recursion_equation_functions(u),null_class)
| function(u) ),
inference(res,[status(thm),theory(equality)],[70,151]),
[iquote('0:Res:70.1,151.0')] ).
cnf(83926,plain,
( ~ member(u,null_class)
| function(v) ),
inference(rew,[status(thm),theory(equality)],[83916,151]),
[iquote('0:Rew:83916.0,151.0')] ).
cnf(84816,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(spr,[status(thm),theory(equality)],[71,9132]),
[iquote('0:SpR:71.1,9132.0')] ).
cnf(84830,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[84816,10]),
[iquote('0:MRR:84816.0,10.0')] ).
cnf(84834,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[84830,11]),
[iquote('0:Res:84830.0,11.0')] ).
cnf(84903,plain,
( ~ member(u,null_class)
| member(v,universal_class) ),
inference(sor,[status(thm)],[3790,83926]),
[iquote('0:SoR:3790.0,83926.1')] ).
cnf(84960,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[35826,84834]),
[iquote('0:Res:35826.0,84834.0')] ).
cnf(84995,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[84960,28]),
[iquote('0:SpL:84960.0,28.1')] ).
cnf(84999,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[84995,84903]),
[iquote('0:MRR:84995.0,84903.1')] ).
cnf(97758,plain,
( ~ subclass(intersection(complement(w__dfg),y__dfg),y__dfg)
| equal(intersection(complement(w__dfg),y__dfg),null_class) ),
inference(res,[status(thm),theory(equality)],[167,181]),
[iquote('0:Res:167.2,181.0')] ).
cnf(97761,plain,
equal(intersection(complement(w__dfg),y__dfg),null_class),
inference(mrr,[status(thm)],[97758,8841]),
[iquote('0:MRR:97758.0,8841.0')] ).
cnf(97821,plain,
( ~ member(u,y__dfg)
| ~ member(u,complement(w__dfg))
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[97761,27]),
[iquote('0:SpR:97761.0,27.2')] ).
cnf(97835,plain,
( ~ member(u,y__dfg)
| ~ member(u,complement(w__dfg)) ),
inference(mrr,[status(thm)],[97821,84999]),
[iquote('0:MRR:97821.2,84999.0')] ).
cnf(98607,plain,
( ~ member(u,universal_class)
| ~ member(u,y__dfg)
| member(u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[29,97835]),
[iquote('0:Res:29.2,97835.1')] ).
cnf(98640,plain,
( ~ member(u,y__dfg)
| member(u,w__dfg) ),
inference(mrr,[status(thm)],[98607,34005]),
[iquote('0:MRR:98607.0,34005.1')] ).
cnf(100582,plain,
( ~ member(not_subclass_element(u,w__dfg),y__dfg)
| subclass(u,w__dfg) ),
inference(res,[status(thm),theory(equality)],[98640,7]),
[iquote('0:Res:98640.1,7.0')] ).
cnf(102289,plain,
( subclass(y__dfg,w__dfg)
| subclass(y__dfg,w__dfg) ),
inference(res,[status(thm),theory(equality)],[6,100582]),
[iquote('0:Res:6.1,100582.0')] ).
cnf(102293,plain,
subclass(y__dfg,w__dfg),
inference(obv,[status(thm),theory(equality)],[102289]),
[iquote('0:Obv:102289.0')] ).
cnf(102294,plain,
$false,
inference(mrr,[status(thm)],[102293,186]),
[iquote('0:MRR:102293.0,186.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM095-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 5 10:09:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 58.03/58.24
% 58.03/58.24 SPASS V 3.9
% 58.03/58.24 SPASS beiseite: Proof found.
% 58.03/58.24 % SZS status Theorem
% 58.03/58.24 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.03/58.24 SPASS derived 84771 clauses, backtracked 18244 clauses, performed 47 splits and kept 49122 clauses.
% 58.03/58.24 SPASS allocated 130595 KBytes.
% 58.03/58.24 SPASS spent 0:0:56.59 on the problem.
% 58.03/58.24 0:00:00.04 for the input.
% 58.03/58.24 0:00:00.00 for the FLOTTER CNF translation.
% 58.03/58.24 0:00:01.06 for inferences.
% 58.03/58.24 0:00:05.16 for the backtracking.
% 58.03/58.24 0:0:49.21 for the reduction.
% 58.03/58.24
% 58.03/58.24
% 58.03/58.24 Here is a proof with depth 6, length 65 :
% 58.03/58.24 % SZS output start Refutation
% See solution above
% 58.03/58.24 Formulae used in the proof : prove_sections_property4_1 prove_sections_property4_2 prove_sections_property4_3 prove_sections_property4_4 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pairs_in_universal ordered_pair cartesian_product1 intersection1 intersection2 intersection3 complement1 complement2 function1 regularity1 regularity2 well_ordering2 section1 recursion_equation_functions1
% 58.03/58.24
%------------------------------------------------------------------------------