TSTP Solution File: SET097-6 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET097-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% 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 : 300s
% DateTime : Fri May 3 02:59:52 EDT 2024
% Result : Unsatisfiable 37.22s 6.21s
% Output : CNFRefutation 37.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of clauses : 85 ( 26 unt; 27 nHn; 70 RR)
% Number of literals : 171 ( 42 equ; 65 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).
cnf(c_50,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).
cnf(c_51,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).
cnf(c_52,plain,
( ~ member(X0,X1)
| ~ subclass(X1,X2)
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(c_53,plain,
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(c_54,plain,
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(c_55,plain,
subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(c_56,plain,
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass1) ).
cnf(c_58,plain,
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(c_59,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(c_63,plain,
unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(c_72,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(c_73,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(c_74,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(c_75,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_76,plain,
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(c_117,plain,
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(c_118,plain,
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(c_144,plain,
subclass(X0,X0),
inference(unflattening,[status(thm)],[c_56]) ).
cnf(c_3673,plain,
( x = null_class
| member(regular(x),x) ),
inference(instantiation,[status(thm)],[c_117]) ).
cnf(c_3777,plain,
( ~ member(regular(x),x)
| ~ subclass(x,X0)
| member(regular(x),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_3778,plain,
( ~ member(regular(x),x)
| ~ subclass(x,universal_class)
| member(regular(x),universal_class) ),
inference(instantiation,[status(thm)],[c_3777]) ).
cnf(c_4243,plain,
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_53,c_72]) ).
cnf(c_4257,plain,
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(superposition,[status(thm)],[c_117,c_75]) ).
cnf(c_4313,plain,
( ~ subclass(X0,X1)
| X0 = null_class
| member(regular(X0),X1) ),
inference(superposition,[status(thm)],[c_117,c_52]) ).
cnf(c_4338,plain,
subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_4243,c_54]) ).
cnf(c_4711,plain,
( X0 = null_class
| subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_118,c_4338]) ).
cnf(c_4744,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[c_49,c_53]) ).
cnf(c_4896,plain,
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[status(thm)],[c_75,c_53]) ).
cnf(c_5056,plain,
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[c_52,c_55]) ).
cnf(c_5064,plain,
( ~ member(X0,intersection(complement(singleton(not_subclass_element(x,null_class))),x))
| member(X0,null_class) ),
inference(resolution,[status(thm)],[c_52,c_4744]) ).
cnf(c_5071,plain,
subclass(x,universal_class),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_5092,plain,
( ~ subclass(X0,null_class)
| X0 = null_class ),
inference(superposition,[status(thm)],[c_4711,c_58]) ).
cnf(c_5243,plain,
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c_5056,c_53]) ).
cnf(c_5571,plain,
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(superposition,[status(thm)],[c_4313,c_4257]) ).
cnf(c_5575,plain,
( ~ subclass(complement(universal_class),universal_class)
| complement(universal_class) = null_class ),
inference(instantiation,[status(thm)],[c_5571]) ).
cnf(c_5712,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(superposition,[status(thm)],[c_53,c_49]) ).
cnf(c_5713,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(superposition,[status(thm)],[c_5712,c_5092]) ).
cnf(c_5748,plain,
( ~ member(X0,null_class)
| member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_5713,c_72]) ).
cnf(c_5893,plain,
( ~ subclass(complement(singleton(not_subclass_element(x,null_class))),X0)
| ~ member(X1,null_class)
| member(X1,X0) ),
inference(superposition,[status(thm)],[c_5748,c_52]) ).
cnf(c_5904,plain,
( ~ member(X0,null_class)
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_55,c_5893]) ).
cnf(c_6340,plain,
subclass(complement(universal_class),X0),
inference(resolution,[status(thm)],[c_4896,c_5243]) ).
cnf(c_6341,plain,
subclass(complement(universal_class),universal_class),
inference(instantiation,[status(thm)],[c_6340]) ).
cnf(c_6655,plain,
( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| ~ member(X0,x)
| member(X0,null_class) ),
inference(resolution,[status(thm)],[c_74,c_5064]) ).
cnf(c_6903,plain,
( ~ member(X0,x)
| ~ member(X0,universal_class)
| member(X0,singleton(not_subclass_element(x,null_class)))
| member(X0,null_class) ),
inference(resolution,[status(thm)],[c_6655,c_76]) ).
cnf(c_7039,plain,
( ~ member(X0,x)
| member(X0,singleton(not_subclass_element(x,null_class)))
| member(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6903,c_5056]) ).
cnf(c_16167,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(superposition,[status(thm)],[c_53,c_49]) ).
cnf(c_16187,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(superposition,[status(thm)],[c_16167,c_5092]) ).
cnf(c_16206,plain,
( ~ member(X0,null_class)
| member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
inference(superposition,[status(thm)],[c_16187,c_72]) ).
cnf(c_16235,plain,
( ~ member(X0,null_class)
| member(X0,x) ),
inference(superposition,[status(thm)],[c_16187,c_73]) ).
cnf(c_16321,plain,
( ~ subclass(complement(singleton(not_subclass_element(x,null_class))),X0)
| ~ member(X1,null_class)
| member(X1,X0) ),
inference(superposition,[status(thm)],[c_16206,c_52]) ).
cnf(c_16325,plain,
( ~ member(X0,null_class)
| member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_55,c_16321]) ).
cnf(c_16467,plain,
( ~ member(X0,null_class)
| X1 = null_class
| member(X0,X1) ),
inference(superposition,[status(thm)],[c_118,c_72]) ).
cnf(c_16579,plain,
( ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| ~ member(X0,x)
| member(X0,null_class) ),
inference(superposition,[status(thm)],[c_16187,c_74]) ).
cnf(c_16639,plain,
( ~ member(X0,x)
| ~ member(X0,universal_class)
| member(X0,singleton(not_subclass_element(x,null_class)))
| member(X0,null_class) ),
inference(superposition,[status(thm)],[c_76,c_16579]) ).
cnf(c_16647,plain,
( ~ member(X0,x)
| member(X0,singleton(not_subclass_element(x,null_class)))
| member(X0,null_class) ),
inference(global_subsumption_just,[status(thm)],[c_16639,c_7039]) ).
cnf(c_16653,plain,
( ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x)
| member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),null_class)
| subclass(X0,singleton(not_subclass_element(x,null_class))) ),
inference(superposition,[status(thm)],[c_16647,c_54]) ).
cnf(c_16699,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(superposition,[status(thm)],[c_63,c_59]) ).
cnf(c_17168,plain,
( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),null_class)
| subclass(x,singleton(not_subclass_element(x,null_class))) ),
inference(superposition,[status(thm)],[c_53,c_16653]) ).
cnf(c_17812,plain,
( not_subclass_element(singleton(X0),X1) = X0
| subclass(singleton(X0),X1) ),
inference(superposition,[status(thm)],[c_53,c_16699]) ).
cnf(c_17825,plain,
( ~ member(X0,x)
| not_subclass_element(x,null_class) = X0
| member(X0,null_class) ),
inference(superposition,[status(thm)],[c_16647,c_16699]) ).
cnf(c_17882,plain,
( not_subclass_element(x,null_class) = regular(x)
| x = null_class
| member(regular(x),null_class) ),
inference(superposition,[status(thm)],[c_117,c_17825]) ).
cnf(c_17896,plain,
( not_subclass_element(x,null_class) = regular(x)
| member(regular(x),null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17882,c_51]) ).
cnf(c_17904,plain,
( ~ subclass(null_class,X0)
| not_subclass_element(x,null_class) = regular(x)
| member(regular(x),X0) ),
inference(superposition,[status(thm)],[c_17896,c_52]) ).
cnf(c_17905,plain,
( not_subclass_element(x,null_class) = regular(x)
| X0 = null_class
| member(regular(x),X0) ),
inference(superposition,[status(thm)],[c_17896,c_16467]) ).
cnf(c_17906,plain,
( not_subclass_element(x,null_class) = regular(x)
| member(regular(x),universal_class) ),
inference(superposition,[status(thm)],[c_17896,c_16325]) ).
cnf(c_17907,plain,
( not_subclass_element(x,null_class) = regular(x)
| member(regular(x),x) ),
inference(superposition,[status(thm)],[c_17896,c_16235]) ).
cnf(c_17915,plain,
member(regular(x),universal_class),
inference(global_subsumption_just,[status(thm)],[c_17906,c_51,c_3673,c_3778,c_5071]) ).
cnf(c_17918,plain,
member(regular(x),x),
inference(global_subsumption_just,[status(thm)],[c_17907,c_51,c_3673]) ).
cnf(c_17930,plain,
( ~ member(regular(x),X0)
| ~ subclass(null_class,complement(X0))
| not_subclass_element(x,null_class) = regular(x) ),
inference(superposition,[status(thm)],[c_17904,c_75]) ).
cnf(c_17958,plain,
( ~ member(regular(x),X0)
| not_subclass_element(x,null_class) = regular(x)
| complement(X0) = null_class ),
inference(superposition,[status(thm)],[c_17905,c_75]) ).
cnf(c_18915,plain,
( not_subclass_element(x,null_class) = regular(x)
| complement(universal_class) = null_class ),
inference(superposition,[status(thm)],[c_17915,c_17958]) ).
cnf(c_20523,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_18915,c_5575,c_6341]) ).
cnf(c_20526,plain,
( ~ member(regular(x),universal_class)
| ~ subclass(null_class,null_class)
| not_subclass_element(x,null_class) = regular(x) ),
inference(superposition,[status(thm)],[c_20523,c_17930]) ).
cnf(c_20545,plain,
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_20523,c_75]) ).
cnf(c_20546,plain,
not_subclass_element(x,null_class) = regular(x),
inference(forward_subsumption_resolution,[status(thm)],[c_20526,c_144,c_17915]) ).
cnf(c_20644,plain,
singleton(regular(x)) != x,
inference(demodulation,[status(thm)],[c_50,c_20546]) ).
cnf(c_20721,plain,
~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_20545,c_5904,c_20545]) ).
cnf(c_20762,plain,
subclass(x,singleton(not_subclass_element(x,null_class))),
inference(backward_subsumption_resolution,[status(thm)],[c_17168,c_20721]) ).
cnf(c_20880,plain,
subclass(x,singleton(regular(x))),
inference(light_normalisation,[status(thm)],[c_20762,c_20546]) ).
cnf(c_20890,plain,
( ~ subclass(singleton(regular(x)),x)
| singleton(regular(x)) = x ),
inference(superposition,[status(thm)],[c_20880,c_58]) ).
cnf(c_20893,plain,
~ subclass(singleton(regular(x)),x),
inference(forward_subsumption_resolution,[status(thm)],[c_20890,c_20644]) ).
cnf(c_21079,plain,
not_subclass_element(singleton(regular(x)),x) = regular(x),
inference(superposition,[status(thm)],[c_17812,c_20893]) ).
cnf(c_21080,plain,
( ~ member(regular(x),x)
| subclass(singleton(regular(x)),x) ),
inference(superposition,[status(thm)],[c_21079,c_54]) ).
cnf(c_21082,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21080,c_20893,c_17918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET097-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 20:47:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 37.22/6.21 % SZS status Started for theBenchmark.p
% 37.22/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 37.22/6.21
% 37.22/6.21 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 37.22/6.21
% 37.22/6.21 ------ iProver source info
% 37.22/6.21
% 37.22/6.21 git: date: 2024-05-02 19:28:25 +0000
% 37.22/6.21 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 37.22/6.21 git: non_committed_changes: false
% 37.22/6.21
% 37.22/6.21 ------ Parsing...successful
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21 ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 37.22/6.21
% 37.22/6.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 37.22/6.21
% 37.22/6.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 37.22/6.21 ------ Proving...
% 37.22/6.21 ------ Problem Properties
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21 clauses 86
% 37.22/6.21 conjectures 3
% 37.22/6.21 EPR 13
% 37.22/6.21 Horn 78
% 37.22/6.21 unary 34
% 37.22/6.21 binary 32
% 37.22/6.21 lits 164
% 37.22/6.21 lits eq 38
% 37.22/6.21 fd_pure 0
% 37.22/6.21 fd_pseudo 0
% 37.22/6.21 fd_cond 3
% 37.22/6.21 fd_pseudo_cond 3
% 37.22/6.21 AC symbols 0
% 37.22/6.21
% 37.22/6.21 ------ Input Options Time Limit: Unbounded
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21 ------
% 37.22/6.21 Current options:
% 37.22/6.21 ------
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21 ------ Proving...
% 37.22/6.21
% 37.22/6.21
% 37.22/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 37.22/6.21
% 37.22/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 37.22/6.21
% 37.22/6.21
%------------------------------------------------------------------------------