TSTP Solution File: SET505-6 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET505-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 : Thu Aug 31 15:08:08 EDT 2023
% Result : Unsatisfiable 51.61s 7.71s
% Output : CNFRefutation 51.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of clauses : 90 ( 35 unt; 16 nHn; 56 RR)
% Number of literals : 166 ( 39 equ; 71 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 129 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,negated_conjecture,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_universal_class_not_set_1) ).
cnf(c_71,plain,
( ~ member(X0,X1)
| ~ subclass(X1,X2)
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(c_72,plain,
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(c_73,plain,
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(c_74,plain,
subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(c_77,plain,
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(c_78,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(c_79,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(c_80,plain,
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(c_82,plain,
unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(c_84,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(c_85,plain,
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(c_86,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(c_87,plain,
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(c_91,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(c_92,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(c_93,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(c_94,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_95,plain,
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(c_96,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
cnf(c_97,plain,
intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',symmetric_difference) ).
cnf(c_98,plain,
intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(c_100,plain,
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(c_136,plain,
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(c_137,plain,
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(c_1316,plain,
intersection(complement(intersection(X0,X1)),union(X0,X1)) = symmetric_difference(X0,X1),
inference(light_normalisation,[status(thm)],[c_97,c_96]) ).
cnf(c_4161,plain,
( ~ member(X0,universal_class)
| member(X0,singleton(X0)) ),
inference(superposition,[status(thm)],[c_82,c_79]) ).
cnf(c_4164,plain,
( ~ member(universal_class,universal_class)
| member(universal_class,singleton(universal_class)) ),
inference(instantiation,[status(thm)],[c_4161]) ).
cnf(c_4182,plain,
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_72,c_91]) ).
cnf(c_4206,plain,
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_72,c_92]) ).
cnf(c_4241,plain,
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_72,c_94]) ).
cnf(c_4382,plain,
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) ),
inference(superposition,[status(thm)],[c_72,c_71]) ).
cnf(c_4552,plain,
member(universal_class,universal_class),
inference(superposition,[status(thm)],[c_49,c_84]) ).
cnf(c_4557,plain,
member(y,universal_class),
inference(superposition,[status(thm)],[c_49,c_85]) ).
cnf(c_4593,plain,
( ~ member(X0,universal_class)
| member(X0,intersection(complement(X1),complement(X2)))
| member(X0,union(X1,X2)) ),
inference(superposition,[status(thm)],[c_96,c_95]) ).
cnf(c_4983,plain,
( ~ subclass(universal_class,X0)
| X0 = universal_class ),
inference(superposition,[status(thm)],[c_74,c_77]) ).
cnf(c_5674,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(superposition,[status(thm)],[c_82,c_78]) ).
cnf(c_5711,plain,
ordered_pair(first(ordered_pair(universal_class,y)),second(ordered_pair(universal_class,y))) = ordered_pair(universal_class,y),
inference(superposition,[status(thm)],[c_49,c_87]) ).
cnf(c_5788,plain,
( ~ member(ordered_pair(universal_class,y),cross_product(X0,X1))
| member(first(ordered_pair(universal_class,y)),X0) ),
inference(superposition,[status(thm)],[c_5711,c_84]) ).
cnf(c_5919,plain,
member(first(ordered_pair(universal_class,y)),universal_class),
inference(superposition,[status(thm)],[c_49,c_5788]) ).
cnf(c_5941,plain,
( ~ member(universal_class,X0)
| ~ member(y,X1)
| member(first(ordered_pair(universal_class,y)),X0) ),
inference(superposition,[status(thm)],[c_86,c_5788]) ).
cnf(c_7664,plain,
( ~ member(X0,universal_class)
| member(X0,union(X1,X2))
| member(X0,complement(X2)) ),
inference(superposition,[status(thm)],[c_4593,c_92]) ).
cnf(c_7952,plain,
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(superposition,[status(thm)],[c_136,c_5674]) ).
cnf(c_11520,plain,
( ~ member(universal_class,X0)
| member(first(ordered_pair(universal_class,y)),X0) ),
inference(superposition,[status(thm)],[c_4557,c_5941]) ).
cnf(c_11542,plain,
( ~ member(first(ordered_pair(universal_class,y)),X0)
| ~ member(universal_class,complement(X0)) ),
inference(superposition,[status(thm)],[c_11520,c_94]) ).
cnf(c_12897,plain,
( ~ member(universal_class,complement(unordered_pair(X0,first(ordered_pair(universal_class,y)))))
| ~ member(first(ordered_pair(universal_class,y)),universal_class) ),
inference(superposition,[status(thm)],[c_80,c_11542]) ).
cnf(c_12898,plain,
( ~ member(universal_class,complement(intersection(X0,X1)))
| ~ member(first(ordered_pair(universal_class,y)),X0)
| ~ member(first(ordered_pair(universal_class,y)),X1) ),
inference(superposition,[status(thm)],[c_93,c_11542]) ).
cnf(c_12980,plain,
~ member(universal_class,complement(unordered_pair(X0,first(ordered_pair(universal_class,y))))),
inference(forward_subsumption_resolution,[status(thm)],[c_12897,c_5919]) ).
cnf(c_13233,plain,
( ~ member(universal_class,universal_class)
| member(universal_class,unordered_pair(X0,first(ordered_pair(universal_class,y)))) ),
inference(superposition,[status(thm)],[c_95,c_12980]) ).
cnf(c_13235,plain,
member(universal_class,unordered_pair(X0,first(ordered_pair(universal_class,y)))),
inference(forward_subsumption_resolution,[status(thm)],[c_13233,c_4552]) ).
cnf(c_13237,plain,
member(universal_class,singleton(first(ordered_pair(universal_class,y)))),
inference(superposition,[status(thm)],[c_82,c_13235]) ).
cnf(c_13245,plain,
first(ordered_pair(universal_class,y)) = universal_class,
inference(superposition,[status(thm)],[c_13237,c_5674]) ).
cnf(c_13248,plain,
member(universal_class,singleton(universal_class)),
inference(demodulation,[status(thm)],[c_13237,c_13245]) ).
cnf(c_17299,plain,
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[status(thm)],[c_7952,c_137]) ).
cnf(c_20464,plain,
subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_4182,c_73]) ).
cnf(c_20608,plain,
subclass(restrict(X0,X1,X2),X0),
inference(superposition,[status(thm)],[c_98,c_20464]) ).
cnf(c_20610,plain,
( X0 = null_class
| subclass(null_class,X0) ),
inference(superposition,[status(thm)],[c_137,c_20464]) ).
cnf(c_20662,plain,
( ~ subclass(X0,null_class)
| X0 = null_class ),
inference(superposition,[status(thm)],[c_20610,c_77]) ).
cnf(c_20885,plain,
restrict(null_class,X0,X1) = null_class,
inference(superposition,[status(thm)],[c_20608,c_20662]) ).
cnf(c_21478,plain,
~ member(X0,domain_of(null_class)),
inference(superposition,[status(thm)],[c_20885,c_100]) ).
cnf(c_21559,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm)],[c_136,c_21478]) ).
cnf(c_21583,plain,
~ member(X0,null_class),
inference(demodulation,[status(thm)],[c_21478,c_21559]) ).
cnf(c_30924,plain,
subclass(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_4206,c_73]) ).
cnf(c_31172,plain,
intersection(X0,null_class) = null_class,
inference(superposition,[status(thm)],[c_30924,c_20662]) ).
cnf(c_33321,plain,
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ),
inference(superposition,[status(thm)],[c_4382,c_4241]) ).
cnf(c_39459,plain,
subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_74,c_33321]) ).
cnf(c_39503,plain,
complement(universal_class) = null_class,
inference(superposition,[status(thm)],[c_39459,c_20662]) ).
cnf(c_39614,plain,
complement(intersection(complement(X0),null_class)) = union(X0,universal_class),
inference(superposition,[status(thm)],[c_39503,c_96]) ).
cnf(c_41338,plain,
union(X0,universal_class) = complement(null_class),
inference(demodulation,[status(thm)],[c_39614,c_31172]) ).
cnf(c_53706,plain,
( ~ member(X0,universal_class)
| member(X0,complement(universal_class))
| member(X0,complement(null_class)) ),
inference(superposition,[status(thm)],[c_41338,c_7664]) ).
cnf(c_53725,plain,
( ~ member(X0,universal_class)
| member(X0,complement(null_class))
| member(X0,null_class) ),
inference(light_normalisation,[status(thm)],[c_53706,c_39503]) ).
cnf(c_53726,plain,
( ~ member(X0,universal_class)
| member(X0,complement(null_class)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53725,c_21583]) ).
cnf(c_54627,plain,
( ~ member(not_subclass_element(X0,complement(null_class)),universal_class)
| subclass(X0,complement(null_class)) ),
inference(superposition,[status(thm)],[c_53726,c_73]) ).
cnf(c_55197,plain,
( ~ subclass(X0,universal_class)
| subclass(X0,complement(null_class)) ),
inference(superposition,[status(thm)],[c_4382,c_54627]) ).
cnf(c_55204,plain,
subclass(X0,complement(null_class)),
inference(forward_subsumption_resolution,[status(thm)],[c_55197,c_74]) ).
cnf(c_55325,plain,
complement(null_class) = universal_class,
inference(superposition,[status(thm)],[c_55204,c_4983]) ).
cnf(c_55374,plain,
union(X0,universal_class) = universal_class,
inference(demodulation,[status(thm)],[c_41338,c_55325]) ).
cnf(c_59275,plain,
intersection(complement(intersection(X0,universal_class)),universal_class) = symmetric_difference(X0,universal_class),
inference(superposition,[status(thm)],[c_55374,c_1316]) ).
cnf(c_66370,plain,
( ~ member(X0,singleton(X1))
| ~ member(X0,X1)
| singleton(X1) = null_class
| member(X0,null_class) ),
inference(superposition,[status(thm)],[c_17299,c_93]) ).
cnf(c_66446,plain,
( ~ member(X0,singleton(X1))
| ~ member(X0,X1)
| singleton(X1) = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[c_66370,c_21583]) ).
cnf(c_66490,plain,
( ~ member(universal_class,singleton(universal_class))
| ~ member(universal_class,universal_class)
| singleton(universal_class) = null_class ),
inference(instantiation,[status(thm)],[c_66446]) ).
cnf(c_131845,plain,
( ~ member(universal_class,complement(intersection(X0,X1)))
| ~ member(universal_class,X0)
| ~ member(universal_class,X1) ),
inference(light_normalisation,[status(thm)],[c_12898,c_13245]) ).
cnf(c_131893,plain,
( ~ member(universal_class,complement(intersection(X0,universal_class)))
| ~ member(universal_class,complement(symmetric_difference(X0,universal_class)))
| ~ member(universal_class,universal_class) ),
inference(superposition,[status(thm)],[c_59275,c_131845]) ).
cnf(c_131930,plain,
( ~ member(universal_class,complement(intersection(X0,universal_class)))
| ~ member(universal_class,complement(symmetric_difference(X0,universal_class))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_131893,c_4552]) ).
cnf(c_135144,plain,
( ~ member(universal_class,complement(symmetric_difference(singleton(universal_class),universal_class)))
| ~ member(universal_class,complement(null_class))
| singleton(universal_class) = null_class ),
inference(superposition,[status(thm)],[c_17299,c_131930]) ).
cnf(c_135168,plain,
( ~ member(universal_class,complement(symmetric_difference(singleton(universal_class),universal_class)))
| ~ member(universal_class,universal_class)
| singleton(universal_class) = null_class ),
inference(light_normalisation,[status(thm)],[c_135144,c_55325]) ).
cnf(c_135169,plain,
( ~ member(universal_class,complement(symmetric_difference(singleton(universal_class),universal_class)))
| singleton(universal_class) = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[c_135168,c_4552]) ).
cnf(c_136271,plain,
singleton(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_135169,c_4164,c_4552,c_66490]) ).
cnf(c_136303,plain,
member(universal_class,null_class),
inference(demodulation,[status(thm)],[c_13248,c_136271]) ).
cnf(c_136304,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_136303,c_21583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET505-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 08:35:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.44 Running first-order theorem proving
% 0.22/0.44 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 51.61/7.71 % SZS status Started for theBenchmark.p
% 51.61/7.71 % SZS status Unsatisfiable for theBenchmark.p
% 51.61/7.71
% 51.61/7.71 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 51.61/7.71
% 51.61/7.71 ------ iProver source info
% 51.61/7.71
% 51.61/7.71 git: date: 2023-05-31 18:12:56 +0000
% 51.61/7.71 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 51.61/7.71 git: non_committed_changes: false
% 51.61/7.71 git: last_make_outside_of_git: false
% 51.61/7.71
% 51.61/7.71 ------ Parsing...successful
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71 ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 51.61/7.71
% 51.61/7.71 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 51.61/7.71
% 51.61/7.71 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 51.61/7.71 ------ Proving...
% 51.61/7.71 ------ Problem Properties
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71 clauses 101
% 51.61/7.71 conjectures 1
% 51.61/7.71 EPR 12
% 51.61/7.71 Horn 93
% 51.61/7.71 unary 40
% 51.61/7.71 binary 40
% 51.61/7.71 lits 189
% 51.61/7.71 lits eq 44
% 51.61/7.71 fd_pure 0
% 51.61/7.71 fd_pseudo 0
% 51.61/7.71 fd_cond 3
% 51.61/7.71 fd_pseudo_cond 7
% 51.61/7.71 AC symbols 0
% 51.61/7.71
% 51.61/7.71 ------ Schedule dynamic 5 is on
% 51.61/7.71
% 51.61/7.71 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71 ------
% 51.61/7.71 Current options:
% 51.61/7.71 ------
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71 ------ Proving...
% 51.61/7.71
% 51.61/7.71
% 51.61/7.71 % SZS status Unsatisfiable for theBenchmark.p
% 51.61/7.71
% 51.61/7.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.61/7.71
% 51.61/7.72
%------------------------------------------------------------------------------