TSTP Solution File: SET155-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET155-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:24:35 EDT 2022
% Result : Unsatisfiable 103.33s 103.51s
% Output : Refutation 103.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 8 unt; 12 nHn; 32 RR)
% Number of literals : 69 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 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(1,axiom,
~ equal(intersection(complement(x__dfg),complement(y__dfg)),complement(union(x__dfg,y__dfg))),
file('SET155-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET155-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET155-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET155-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET155-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET155-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET155-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET155-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET155-6.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET155-6.p',unknown),
[] ).
cnf(120,plain,
( ~ subclass(complement(union(x__dfg,y__dfg)),intersection(complement(x__dfg),complement(y__dfg)))
| ~ subclass(intersection(complement(x__dfg),complement(y__dfg)),complement(union(x__dfg,y__dfg))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(155,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[3,25]),
[iquote('0:Res:3.1,25.1')] ).
cnf(212,plain,
( ~ member(u,intersection(complement(v),complement(w)))
| ~ member(u,union(v,w)) ),
inference(spl,[status(thm),theory(equality)],[27,25]),
[iquote('0:SpL:27.0,25.1')] ).
cnf(279,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(356,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.1,2.0')] ).
cnf(786,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(1296,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[26,155]),
[iquote('0:Res:26.2,155.0')] ).
cnf(4898,plain,
( ~ member(not_subclass_element(intersection(complement(u),complement(v)),w),union(u,v))
| subclass(intersection(complement(u),complement(v)),w) ),
inference(res,[status(thm),theory(equality)],[3,212]),
[iquote('0:Res:3.1,212.0')] ).
cnf(8260,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[356,279]),
[iquote('0:Res:356.2,279.0')] ).
cnf(8264,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[8260]),
[iquote('0:Obv:8260.1')] ).
cnf(8265,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[8264,5]),
[iquote('0:MRR:8264.0,5.0')] ).
cnf(8787,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[5,786]),
[iquote('0:Res:5.0,786.2')] ).
cnf(8797,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[8787]),
[iquote('0:Con:8787.1')] ).
cnf(8849,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[3,8797]),
[iquote('0:Res:3.1,8797.0')] ).
cnf(8966,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1296,8849]),
[iquote('0:MRR:1296.0,8849.1')] ).
cnf(20753,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[8966,4]),
[iquote('0:Res:8966.0,4.0')] ).
cnf(20756,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[20753]),
[iquote('0:Obv:20753.0')] ).
cnf(20786,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[27,20756]),
[iquote('0:SpR:27.0,20756.0')] ).
cnf(20812,plain,
~ subclass(intersection(complement(x__dfg),complement(y__dfg)),complement(union(x__dfg,y__dfg))),
inference(mrr,[status(thm)],[120,20786]),
[iquote('0:MRR:120.0,20786.0')] ).
cnf(97153,plain,
( subclass(intersection(complement(u),complement(v)),complement(union(u,v)))
| subclass(intersection(complement(u),complement(v)),complement(union(u,v))) ),
inference(res,[status(thm),theory(equality)],[8265,4898]),
[iquote('0:Res:8265.0,4898.0')] ).
cnf(97171,plain,
subclass(intersection(complement(u),complement(v)),complement(union(u,v))),
inference(obv,[status(thm),theory(equality)],[97153]),
[iquote('0:Obv:97153.0')] ).
cnf(97172,plain,
$false,
inference(unc,[status(thm)],[97171,20812]),
[iquote('0:UnC:97171.0,20812.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET155-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 10 21:31:55 EDT 2022
% 0.11/0.32 % CPUTime :
% 103.33/103.51
% 103.33/103.51 SPASS V 3.9
% 103.33/103.51 SPASS beiseite: Proof found.
% 103.33/103.51 % SZS status Theorem
% 103.33/103.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 103.33/103.51 SPASS derived 70578 clauses, backtracked 239 clauses, performed 8 splits and kept 23596 clauses.
% 103.33/103.51 SPASS allocated 156844 KBytes.
% 103.33/103.51 SPASS spent 0:1:41.48 on the problem.
% 103.33/103.51 0:00:00.04 for the input.
% 103.33/103.51 0:00:00.00 for the FLOTTER CNF translation.
% 103.33/103.51 0:00:00.86 for inferences.
% 103.33/103.51 0:0:11.75 for the backtracking.
% 103.33/103.51 0:1:27.98 for the reduction.
% 103.33/103.51
% 103.33/103.51
% 103.33/103.51 Here is a proof with depth 4, length 32 :
% 103.33/103.51 % SZS output start Refutation
% See solution above
% 103.33/103.51 Formulae used in the proof : prove_demorgans_law1_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection3 complement1 complement2 union
% 103.33/103.51
%------------------------------------------------------------------------------