%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET182-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:46:51 PM UTC 2026
% Result : Unsatisfiable 82.23s 18.86s
% Output : CNFRefutation 82.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 28
% Syntax : Number of formulae : 178 ( 41 unt; 7 def)
% Number of atoms : 541 ( 55 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 311 ( 128 ~; 183 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 226 ( 0 sgn 226 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',function1) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
union(intersection(complement(x),y),intersection(x,y)) != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distribution_property3_1) ).
fof(f123,plain,
y != union(intersection(complement(x),y),intersection(x,y)),
inference(reorient_equations,[],[f122]) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f15,f128]) ).
fof(f186,plain,
y != complement(intersection(complement(intersection(complement(x),y)),complement(intersection(x,y)))),
inference(definition_unfolding,[],[f123,f26]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_165,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_210,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_214,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_215,plain,
! [X0: $i] :
( ( X0 = null_class )
| ( intersection(X0,regular(X0)) = null_class ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_255,negated_conjecture,
complement(intersection(complement(intersection(complement(x),y)),complement(intersection(x,y)))) != y,
inference(cnf_transformation,[],[f186]) ).
tcf(c_2974,definition,
iPr_def_10 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,definition,
iPr_def_11 = intersection(iPr_def_10,y),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2976,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2977,definition,
iPr_def_13 = intersection(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2978,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2979,definition,
iPr_def_15 = intersection(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2980,definition,
iPr_def_16 = complement(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_2981,negated_conjecture,
iPr_def_16 != y,
inference(demodulation,[status(thm)],[c_255,c_2977,c_2978,c_2974,c_2975,c_2976,c_2979,c_2980]) ).
tcf(c_3889,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_163,c_180]) ).
tcf(c_3977,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_163,c_181]) ).
tcf(c_3984,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_2979,c_181]) ).
tcf(c_4012,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_163,c_183]) ).
tcf(c_4013,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_214,c_183]) ).
tcf(c_4016,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2978,c_183]) ).
tcf(c_4034,plain,
( ( complement(universal_class) = null_class )
| ~ member(regular(complement(universal_class)),universal_class) ),
inference(instantiation,[status(thm)],[c_4013]) ).
tcf(c_4171,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_4221,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,x)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2974,c_184]) ).
tcf(c_4222,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,iPr_def_11)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2976,c_184]) ).
tcf(c_4223,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2978,c_184]) ).
tcf(c_4224,plain,
! [X0: $i] :
( member(X0,iPr_def_16)
| member(X0,iPr_def_15)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2980,c_184]) ).
tcf(c_4316,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_4171]) ).
tcf(c_4362,plain,
( ( iPr_def_16 = y )
| ~ subclass(iPr_def_16,y)
| ~ subclass(y,iPr_def_16) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_4465,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| ~ member(X0,y)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_2977,c_182]) ).
tcf(c_5006,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_10)
| member(not_subclass_element(X0,X1),x) ),
inference(superposition,[status(thm)],[c_4316,c_4221]) ).
tcf(c_5186,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_12)
| member(not_subclass_element(X0,X1),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4316,c_4222]) ).
tcf(c_5267,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_14)
| member(not_subclass_element(X0,X1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_4316,c_4223]) ).
tcf(c_5357,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_16)
| member(not_subclass_element(X0,X1),iPr_def_15) ),
inference(superposition,[status(thm)],[c_4316,c_4224]) ).
tcf(c_5686,plain,
! [X0: $i] : subclass(complement(universal_class),X0),
inference(superposition,[status(thm)],[c_4316,c_4012]) ).
tcf(c_5728,plain,
! [X0: $i] :
( ( complement(universal_class) = X0 )
| ~ subclass(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_5686,c_168]) ).
tcf(c_5729,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,complement(universal_class)) ),
inference(superposition,[status(thm)],[c_5686,c_162]) ).
tcf(c_5763,plain,
! [X0: $i] :
( member(regular(complement(universal_class)),X0)
| ( complement(universal_class) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_5729]) ).
tcf(c_5770,plain,
( member(regular(complement(universal_class)),universal_class)
| ( complement(universal_class) = null_class ) ),
inference(instantiation,[status(thm)],[c_5763]) ).
tcf(c_5950,plain,
complement(universal_class) = null_class,
inference(global_subsumption_just,[status(thm)],[c_5763,c_4034,c_5770]) ).
tcf(c_5952,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(demodulation,[status(thm)],[c_5728,c_5950]) ).
tcf(c_5953,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(demodulation,[status(thm)],[c_5729,c_5950]) ).
tcf(c_5965,plain,
! [X0: $i] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_5950,c_183]) ).
tcf(c_5974,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_5953,c_4171,c_5953,c_5965]) ).
tcf(c_6525,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = null_class )
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_215,c_180]) ).
tcf(c_6919,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(iPr_def_13,X0),X1)
| ~ member(not_subclass_element(intersection(iPr_def_13,X0),X1),iPr_def_14) ),
inference(superposition,[status(thm)],[c_3889,c_4016]) ).
tcf(c_8144,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,iPr_def_15),X1)
| member(not_subclass_element(intersection(X0,iPr_def_15),X1),iPr_def_14) ),
inference(superposition,[status(thm)],[c_3977,c_3984]) ).
tcf(c_8281,plain,
( subclass(iPr_def_16,y)
| ~ member(not_subclass_element(iPr_def_16,y),y) ),
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_15543,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_6525,c_4171,c_5953,c_5965]) ).
tcf(c_15545,plain,
! [X0: $i] : subclass(null_class,X0),
inference(superposition,[status(thm)],[c_163,c_15543]) ).
tcf(c_25278,plain,
! [X0: $i] :
( subclass(X0,x)
| member(not_subclass_element(X0,x),iPr_def_10) ),
inference(superposition,[status(thm)],[c_5006,c_164]) ).
tcf(c_25517,plain,
! [X0: $i] :
( subclass(X0,iPr_def_12)
| member(not_subclass_element(X0,iPr_def_12),iPr_def_11) ),
inference(superposition,[status(thm)],[c_5186,c_164]) ).
tcf(c_34586,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_13) ),
inference(superposition,[status(thm)],[c_5267,c_164]) ).
tcf(c_40777,plain,
! [X0: $i] :
( subclass(X0,iPr_def_16)
| member(not_subclass_element(X0,iPr_def_16),iPr_def_15) ),
inference(superposition,[status(thm)],[c_5357,c_164]) ).
tcf(c_44954,plain,
! [X0: $i] : subclass(intersection(iPr_def_13,iPr_def_15),X0),
inference(superposition,[status(thm)],[c_8144,c_6919]) ).
tcf(c_45131,plain,
intersection(iPr_def_13,iPr_def_15) = null_class,
inference(superposition,[status(thm)],[c_44954,c_5952]) ).
tcf(c_45255,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,iPr_def_15)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_45131,c_182]) ).
tcf(c_45307,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_15)
| ~ member(X0,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45255,c_5974]) ).
tcf(c_147820,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_163,c_180]) ).
tcf(c_147821,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_180]) ).
tcf(c_147826,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_2979,c_180]) ).
tcf(c_147892,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_163,c_181]) ).
tcf(c_147893,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_214,c_181]) ).
tcf(c_147894,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_2977,c_181]) ).
tcf(c_147898,plain,
! [X0: $i] :
( member(X0,y)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2975,c_181]) ).
tcf(c_147921,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_163,c_183]) ).
tcf(c_147924,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2976,c_183]) ).
tcf(c_147926,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_16)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_2980,c_183]) ).
tcf(c_148027,plain,
! [X0: $i] :
( subclass(iPr_def_11,X0)
| ~ member(not_subclass_element(iPr_def_11,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_163,c_147924]) ).
tcf(c_148055,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_165,c_162]) ).
tcf(c_148061,plain,
! [X0: $i,X1: $i] :
( member(X0,cross_product(universal_class,universal_class))
| ~ function(X1)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_210,c_162]) ).
tcf(c_148066,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_15545,c_162]) ).
tcf(c_148098,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,x)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2974,c_184]) ).
tcf(c_148099,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,iPr_def_11)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2976,c_184]) ).
tcf(c_148100,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2978,c_184]) ).
tcf(c_148101,plain,
! [X0: $i] :
( member(X0,iPr_def_16)
| member(X0,iPr_def_15)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_2980,c_184]) ).
tcf(c_148186,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_163,c_148055]) ).
tcf(c_148217,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(global_subsumption_just,[status(thm)],[c_148066,c_4171,c_5953,c_5965]) ).
tcf(c_148315,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_2975,c_182]) ).
tcf(c_148316,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2979,c_182]) ).
tcf(c_149438,plain,
! [X0: $i] :
( subclass(complement(iPr_def_15),X0)
| ~ member(not_subclass_element(iPr_def_16,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_2980,c_147921]) ).
tcf(c_149439,plain,
! [X0: $i] :
( subclass(iPr_def_16,X0)
| ~ member(not_subclass_element(iPr_def_16,X0),iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_149438,c_2980]) ).
tcf(c_151206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(unordered_pair(X0,X1),X2) = null_class )
| ( regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
| ( regular(intersection(unordered_pair(X0,X1),X2)) = X0 ) ),
inference(superposition,[status(thm)],[c_147821,c_169]) ).
tcf(c_151524,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,iPr_def_15),X1)
| ~ member(not_subclass_element(intersection(X0,iPr_def_15),X1),iPr_def_16) ),
inference(superposition,[status(thm)],[c_147892,c_147926]) ).
tcf(c_152080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(unordered_pair(X1,X0),X2) = null_class )
| ( regular(intersection(unordered_pair(X1,X0),X2)) = X0 )
| ( X0 != X1 ) ),
inference(equality_factoring,[status(thm)],[c_151206]) ).
tcf(c_152160,plain,
! [X0: $i,X1: $i] :
( member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_172,c_148061]) ).
tcf(c_152645,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152160,c_174]) ).
tcf(c_152669,plain,
! [X0: $i] :
( member(X0,iPr_def_16)
| member(X0,iPr_def_15)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152645,c_148101]) ).
tcf(c_152670,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152645,c_148100]) ).
tcf(c_152671,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,iPr_def_11)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152645,c_148099]) ).
tcf(c_152672,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,x)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152645,c_148098]) ).
tcf(c_152790,plain,
! [X0: $i] :
( subclass(X0,iPr_def_16)
| member(not_subclass_element(X0,iPr_def_16),iPr_def_15)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152669,c_164]) ).
tcf(c_152844,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_13)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152670,c_164]) ).
tcf(c_152935,plain,
! [X0: $i] :
( subclass(X0,iPr_def_12)
| member(not_subclass_element(X0,iPr_def_12),iPr_def_11)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152671,c_164]) ).
tcf(c_152983,plain,
! [X0: $i] :
( subclass(X0,x)
| member(not_subclass_element(X0,x),iPr_def_10)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_152672,c_164]) ).
tcf(c_153406,plain,
! [X0: $i] :
( subclass(X0,iPr_def_16)
| member(not_subclass_element(X0,iPr_def_16),iPr_def_15) ),
inference(global_subsumption_just,[status(thm)],[c_152790,c_40777]) ).
tcf(c_153416,plain,
! [X0: $i] :
( subclass(X0,iPr_def_16)
| member(not_subclass_element(X0,iPr_def_16),iPr_def_12) ),
inference(superposition,[status(thm)],[c_153406,c_147826]) ).
tcf(c_153468,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_152844,c_34586]) ).
tcf(c_153477,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),y) ),
inference(superposition,[status(thm)],[c_153468,c_147894]) ).
tcf(c_153542,plain,
! [X0: $i] :
( subclass(X0,iPr_def_12)
| member(not_subclass_element(X0,iPr_def_12),iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_152935,c_25517]) ).
tcf(c_153551,plain,
! [X0: $i] :
( subclass(X0,iPr_def_12)
| member(not_subclass_element(X0,iPr_def_12),y) ),
inference(superposition,[status(thm)],[c_153542,c_147898]) ).
tcf(c_153605,plain,
! [X0: $i] :
( subclass(X0,x)
| member(not_subclass_element(X0,x),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_152983,c_25278]) ).
tcf(c_153613,plain,
! [X0: $i] :
( subclass(X0,x)
| member(not_subclass_element(X0,x),iPr_def_11)
| ~ member(not_subclass_element(X0,x),y) ),
inference(superposition,[status(thm)],[c_153605,c_148315]) ).
tcf(c_153803,plain,
subclass(iPr_def_11,iPr_def_16),
inference(superposition,[status(thm)],[c_153416,c_148027]) ).
tcf(c_153816,plain,
! [X0: $i] :
( member(X0,iPr_def_16)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_153803,c_162]) ).
tcf(c_153960,plain,
subclass(complement(y),iPr_def_14),
inference(superposition,[status(thm)],[c_153477,c_147921]) ).
tcf(c_154444,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,complement(y)) ),
inference(superposition,[status(thm)],[c_153960,c_162]) ).
tcf(c_154627,plain,
subclass(complement(y),iPr_def_12),
inference(superposition,[status(thm)],[c_153551,c_147921]) ).
tcf(c_154632,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,complement(y)) ),
inference(superposition,[status(thm)],[c_154627,c_162]) ).
tcf(c_154833,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,y)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_184,c_154444]) ).
tcf(c_155194,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,y)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_184,c_154632]) ).
tcf(c_157026,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_14)
| member(not_subclass_element(X0,X1),y) ),
inference(superposition,[status(thm)],[c_148186,c_154833]) ).
tcf(c_157334,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_12)
| member(not_subclass_element(X0,X1),y) ),
inference(superposition,[status(thm)],[c_148186,c_155194]) ).
tcf(c_157638,plain,
! [X0: $i,X1: $i] :
( ( intersection(unordered_pair(X0,X0),X1) = null_class )
| ( regular(intersection(unordered_pair(X0,X0),X1)) = X0 ) ),
inference(equality_resolution,[status(thm)],[c_152080]) ).
tcf(c_203134,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( intersection(unordered_pair(X0,X0),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_157638,c_147893]) ).
tcf(c_203767,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ( intersection(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),X1) = null_class ) ),
inference(superposition,[status(thm)],[c_203134,c_164]) ).
tcf(c_264913,plain,
! [X0: $i] :
( subclass(intersection(y,X0),x)
| member(not_subclass_element(intersection(y,X0),x),iPr_def_11) ),
inference(superposition,[status(thm)],[c_147820,c_153613]) ).
tcf(c_265359,plain,
! [X0: $i] :
( subclass(intersection(y,X0),x)
| member(not_subclass_element(intersection(y,X0),x),iPr_def_16) ),
inference(superposition,[status(thm)],[c_264913,c_153816]) ).
tcf(c_267304,plain,
subclass(intersection(y,iPr_def_15),x),
inference(superposition,[status(thm)],[c_265359,c_151524]) ).
tcf(c_267346,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,intersection(y,iPr_def_15)) ),
inference(superposition,[status(thm)],[c_267304,c_162]) ).
tcf(c_267360,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_15)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_182,c_267346]) ).
tcf(c_267426,plain,
! [X0: $i] :
( ~ member(X0,y)
| ~ member(X0,iPr_def_15) ),
inference(global_subsumption_just,[status(thm)],[c_267360,c_4465,c_45307,c_267360]) ).
tcf(c_267427,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_15)
| ~ member(X0,y) ),
inference(renaming,[status(thm)],[c_267426]) ).
tcf(c_267452,plain,
! [X0: $i] :
( subclass(X0,iPr_def_16)
| ~ member(not_subclass_element(X0,iPr_def_16),y) ),
inference(superposition,[status(thm)],[c_153406,c_267427]) ).
tcf(c_267611,plain,
subclass(y,iPr_def_16),
inference(superposition,[status(thm)],[c_163,c_267452]) ).
tcf(c_267656,plain,
( ( y = iPr_def_16 )
| ~ subclass(iPr_def_16,y) ),
inference(superposition,[status(thm)],[c_267611,c_168]) ).
tcf(c_267846,plain,
~ subclass(iPr_def_16,y),
inference(global_subsumption_just,[status(thm)],[c_267656,c_2981,c_4362,c_267611]) ).
tcf(c_284636,plain,
intersection(unordered_pair(not_subclass_element(iPr_def_16,y),not_subclass_element(iPr_def_16,y)),y) = null_class,
inference(superposition,[status(thm)],[c_203767,c_267846]) ).
tcf(c_285405,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,y)
| ~ member(X0,unordered_pair(not_subclass_element(iPr_def_16,y),not_subclass_element(iPr_def_16,y))) ),
inference(superposition,[status(thm)],[c_284636,c_182]) ).
tcf(c_285430,plain,
! [X0: $i] :
( ~ member(X0,y)
| ~ member(X0,unordered_pair(not_subclass_element(iPr_def_16,y),not_subclass_element(iPr_def_16,y))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_285405,c_148217]) ).
tcf(c_286217,plain,
( ~ member(not_subclass_element(iPr_def_16,y),universal_class)
| ~ member(not_subclass_element(iPr_def_16,y),y) ),
inference(superposition,[status(thm)],[c_170,c_285430]) ).
tcf(c_286266,plain,
~ member(not_subclass_element(iPr_def_16,y),y),
inference(global_subsumption_just,[status(thm)],[c_286217,c_2981,c_4362,c_8281,c_267611]) ).
tcf(c_286281,plain,
( subclass(iPr_def_16,y)
| member(not_subclass_element(iPr_def_16,y),iPr_def_12) ),
inference(superposition,[status(thm)],[c_157334,c_286266]) ).
tcf(c_286282,plain,
( subclass(iPr_def_16,y)
| member(not_subclass_element(iPr_def_16,y),iPr_def_14) ),
inference(superposition,[status(thm)],[c_157026,c_286266]) ).
tcf(c_286283,plain,
member(not_subclass_element(iPr_def_16,y),iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_286282,c_267846]) ).
tcf(c_286284,plain,
member(not_subclass_element(iPr_def_16,y),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_286281,c_267846]) ).
tcf(c_286424,plain,
( member(not_subclass_element(iPr_def_16,y),iPr_def_15)
| ~ member(not_subclass_element(iPr_def_16,y),iPr_def_14) ),
inference(superposition,[status(thm)],[c_286284,c_148316]) ).
tcf(c_286427,plain,
member(not_subclass_element(iPr_def_16,y),iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_286424,c_286283]) ).
tcf(c_286458,plain,
subclass(iPr_def_16,y),
inference(superposition,[status(thm)],[c_286427,c_149439]) ).
tcf(c_286459,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_286458,c_267846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET182-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n012.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 10:09:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.39 Running first-order theorem proving
% 0.07/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.40
% 0.07/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.40
% 0.07/0.40 % Detected problem language: tptp
% 0.07/0.41 % Proving...
% 82.23/18.86 % SZS status Started for theBenchmark.p
% 82.23/18.86 % SZS status Unsatisfiable for theBenchmark.p
% 82.23/18.86
% 82.23/18.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 82.23/18.86
% 82.23/18.86 % ------ iProver source info
% 82.23/18.86
% 82.23/18.86 % git: date: 2026-07-19 20:42:38 +0200
% 82.23/18.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 82.23/18.86 % git: non_committed_changes: false
% 82.23/18.86
% 82.23/18.86 % ------ Parsing...% successful
% 82.23/18.86
% 82.23/18.86
% 82.23/18.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 82.23/18.86
% 82.23/18.86 % ------ Preprocessing... sup_sim: 0 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 %
% 82.23/18.86
% 82.23/18.86 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 82.23/18.86
% 82.23/18.86 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 82.23/18.86 % ------ Proving...
% 82.23/18.86 % ------ Problem Properties
% 82.23/18.86
% 82.23/18.86 %
% 82.23/18.86 % clauses 89
% 82.23/18.86 % conjectures 1
% 82.23/18.86 % EPR 13
% 82.23/18.86 % Horn 81
% 82.23/18.86 % unary 28
% 82.23/18.86 % binary 40
% 82.23/18.86 % lits 177
% 82.23/18.86 % lits eq 33
% 82.23/18.86 % fd_pure 0
% 82.23/18.86 % fd_pseudo 0
% 82.23/18.86 % fd_cond 3
% 82.23/18.86 % fd_pseudo_cond 7
% 82.23/18.86 % AC symbols 0
% 82.23/18.86
% 82.23/18.86 % ------ Schedule dynamic 5 is on
% 82.23/18.86
% 82.23/18.86 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 82.23/18.86
% 82.23/18.86
% 82.23/18.86 % ------
% 82.23/18.86 % Current options:
% 82.23/18.86 % ------
% 82.23/18.86
% 82.23/18.86
% 82.23/18.86 %
% 82.23/18.86
% 82.23/18.86 % ------ Proving...
% 82.23/18.86 % Proof_search_loop: time out after: 5141 full_loop iterations
% 82.23/18.86
% 82.23/18.86 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 82.23/18.86
% 82.23/18.86
% 82.23/18.86 % ------
% 82.23/18.86 % Current options:
% 82.23/18.86 % ------
% 82.23/18.86
% 82.23/18.86
% 82.23/18.86 %
% 82.23/18.86
% 82.23/18.86 % ------ Proving...
% 82.23/18.86 %
% 82.23/18.86
% 82.23/18.86 % SZS status Unsatisfiable for theBenchmark.p
% 82.23/18.86
% 82.23/18.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 82.23/18.86
% 82.23/18.86
%------------------------------------------------------------------------------