%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM058-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 02:23:18 PM UTC 2026
% Result : Unsatisfiable 89.87s 15.16s
% Output : CNFRefutation 89.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 28
% Syntax : Number of formulae : 119 ( 52 unt; 4 def)
% Number of atoms : 286 ( 74 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 141 ( 67 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 172 ( 0 sgn 172 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
fof(f30,axiom,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
fof(f63,axiom,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function1) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f133,axiom,
! [X2,X0,X1] : segment(X0,X1,X2) = domain_of(restrict(X0,X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',segment) ).
fof(f163,axiom,
! [X0,X1] :
( function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',recursion_equation_functions1) ).
fof(f176,negated_conjecture,
~ member(z,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_segments_property2_1) ).
fof(f177,negated_conjecture,
segment(xr,y,z) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_segments_property2_2) ).
fof(f178,plain,
null_class != segment(xr,y,z),
inference(reorient_equations,[],[f177]) ).
fof(f179,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(f193,plain,
! [X2,X0,X1] : segment(X0,X1,X2) = domain_of(intersection(X0,cross_product(X1,unordered_pair(X2,X2)))),
inference(definition_unfolding,[],[f133,f28,f12]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f14,f179]) ).
fof(f197,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,f179]) ).
fof(f199,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f179]) ).
fof(f202,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f203,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f269,plain,
null_class != domain_of(intersection(xr,cross_product(y,unordered_pair(z,z)))),
inference(definition_unfolding,[],[f178,f193]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_212,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f11]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_221,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,[],[f197]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f202]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != null_class ) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_249,plain,
member(omega,universal_class),
inference(cnf_transformation,[],[f53]) ).
tcf(c_257,plain,
! [X0: $i] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_261,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] :
( function(X1)
| ~ member(X0,recursion_equation_functions(X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_344,negated_conjecture,
~ member(z,universal_class),
inference(cnf_transformation,[],[f176]) ).
tcf(c_345,negated_conjecture,
domain_of(intersection(xr,cross_product(y,unordered_pair(z,z)))) != null_class,
inference(cnf_transformation,[],[f269]) ).
tcf(c_4628,definition,
iPr_def_10 = unordered_pair(z,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4629,definition,
iPr_def_11 = cross_product(y,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4630,definition,
iPr_def_12 = intersection(xr,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4631,definition,
iPr_def_13 = domain_of(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4632,negated_conjecture,
iPr_def_13 != null_class,
inference(demodulation,[status(thm)],[c_345,c_4628,c_4629,c_4630,c_4631]) ).
tcf(c_4633,negated_conjecture,
~ member(z,universal_class),
inference(demodulation,[status(thm)],[c_344]) ).
tcf(c_5834,plain,
! [X0: $i] : intersection(X0,iPr_def_11) = intersection(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_4629,c_232]) ).
tcf(c_5884,plain,
! [X0: $i] :
( function(X0)
| ( recursion_equation_functions(X0) = null_class ) ),
inference(superposition,[status(thm)],[c_261,c_334]) ).
tcf(c_5925,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = null_class ) ),
inference(superposition,[status(thm)],[c_261,c_227]) ).
tcf(c_6293,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_219,c_209]) ).
tcf(c_6992,plain,
! [X0: $i] :
( ( X0 = z )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4628,c_216]) ).
tcf(c_7026,plain,
( ( null_class = iPr_def_10 )
| ( regular(iPr_def_10) = z ) ),
inference(superposition,[status(thm)],[c_261,c_6992]) ).
tcf(c_7230,plain,
( member(z,iPr_def_10)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_7026,c_261]) ).
tcf(c_7245,plain,
! [X0: $i] :
( member(z,X0)
| ( null_class = iPr_def_10 )
| ~ subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_7230,c_209]) ).
tcf(c_7300,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X0)
| ~ subclass(universal_class,cross_product(X0,X1)) ),
inference(superposition,[status(thm)],[c_6293,c_220]) ).
tcf(c_7398,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_257,c_7300]) ).
tcf(c_7410,plain,
~ function(universal_class),
inference(superposition,[status(thm)],[c_7398,c_4633]) ).
tcf(c_7414,plain,
recursion_equation_functions(universal_class) = null_class,
inference(superposition,[status(thm)],[c_5884,c_7410]) ).
tcf(c_7419,plain,
! [X0: $i] :
( function(universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_7414,c_334]) ).
tcf(c_7427,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[c_7419,c_7410]) ).
tcf(c_13408,plain,
( member(z,universal_class)
| ( null_class = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_212,c_7245]) ).
tcf(c_13413,plain,
null_class = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_13408,c_4633]) ).
tcf(c_13513,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_7427,c_13413]) ).
tcf(c_13540,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_5925,c_13413]) ).
tcf(c_14812,plain,
! [X0: $i] :
( member(regular(intersection(X0,iPr_def_11)),iPr_def_11)
| ( intersection(iPr_def_11,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_5834,c_13540]) ).
tcf(c_15825,plain,
! [X0: $i] :
( ( X0 = z )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4628,c_216]) ).
tcf(c_16173,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_15825,c_13513]) ).
tcf(c_16176,plain,
null_class = iPr_def_10,
inference(superposition,[status(thm)],[c_261,c_16173]) ).
tcf(c_23013,plain,
! [X0: $i] :
( member(regular(intersection(iPr_def_11,X0)),iPr_def_11)
| ( intersection(iPr_def_11,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_5834,c_14812]) ).
tcf(c_105757,plain,
iPr_def_10 != iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4632,c_16176]) ).
tcf(c_105766,plain,
! [X0: $i] : intersection(X0,iPr_def_11) = intersection(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_4629,c_232]) ).
tcf(c_105768,plain,
intersection(iPr_def_11,xr) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4630,c_105766]) ).
tcf(c_105799,plain,
! [X0: $i,X1: $i] :
( function(X0)
| subclass(recursion_equation_functions(X0),X1) ),
inference(superposition,[status(thm)],[c_210,c_334]) ).
tcf(c_105814,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_261,c_16176]) ).
tcf(c_105823,plain,
! [X0: $i] :
( function(X0)
| ( recursion_equation_functions(X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_105814,c_334]) ).
tcf(c_105885,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_210,c_227]) ).
tcf(c_105886,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_105814,c_227]) ).
tcf(c_105940,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_105814,c_228]) ).
tcf(c_106109,plain,
! [X0: $i] :
( member(omega,X0)
| ~ subclass(universal_class,X0) ),
inference(superposition,[status(thm)],[c_249,c_209]) ).
tcf(c_106205,plain,
( member(omega,cross_product(universal_class,universal_class))
| ~ function(universal_class) ),
inference(superposition,[status(thm)],[c_257,c_106109]) ).
tcf(c_106378,plain,
~ function(universal_class),
inference(global_subsumption_just,[status(thm)],[c_106205,c_7410]) ).
tcf(c_106380,plain,
recursion_equation_functions(universal_class) = iPr_def_10,
inference(superposition,[status(thm)],[c_105823,c_106378]) ).
tcf(c_106383,plain,
! [X0: $i] :
( function(universal_class)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_106380,c_334]) ).
tcf(c_106384,plain,
! [X0: $i] :
( function(universal_class)
| subclass(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_106380,c_105799]) ).
tcf(c_106385,plain,
! [X0: $i] : subclass(iPr_def_10,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_106384,c_106378]) ).
tcf(c_106386,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_106383,c_106378]) ).
tcf(c_106387,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ subclass(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_106385,c_215]) ).
tcf(c_106774,plain,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_233,c_16176]) ).
tcf(c_106904,plain,
! [X0: $i,X1: $i] :
( member(X1,iPr_def_10)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_11) ),
inference(superposition,[status(thm)],[c_4629,c_221]) ).
tcf(c_106907,plain,
! [X0: $i,X1: $i] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_106904,c_106386]) ).
tcf(c_108197,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_105885,c_211]) ).
tcf(c_108336,plain,
! [X0: $i] : intersection(iPr_def_10,X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_108197,c_106387]) ).
tcf(c_108376,plain,
! [X0: $i] : ~ member(X0,domain_of(iPr_def_10)),
inference(superposition,[status(thm)],[c_108336,c_106774]) ).
tcf(c_108390,plain,
domain_of(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_105814,c_108376]) ).
tcf(c_109264,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( intersection(cross_product(X0,X1),X2) = iPr_def_10 )
| ( unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) = regular(intersection(cross_product(X0,X1),X2)) ) ),
inference(superposition,[status(thm)],[c_105886,c_223]) ).
tcf(c_109929,plain,
! [X0: $i] :
( member(regular(intersection(X0,iPr_def_11)),X0)
| ( intersection(iPr_def_11,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_105766,c_105940]) ).
tcf(c_113873,plain,
! [X0: $i] :
( ( intersection(cross_product(y,iPr_def_10),X0) = iPr_def_10 )
| ( unordered_pair(unordered_pair(first(regular(intersection(iPr_def_11,X0))),first(regular(intersection(iPr_def_11,X0)))),unordered_pair(first(regular(intersection(iPr_def_11,X0))),unordered_pair(second(regular(intersection(iPr_def_11,X0))),second(regular(intersection(iPr_def_11,X0)))))) = regular(intersection(iPr_def_11,X0)) ) ),
inference(superposition,[status(thm)],[c_4629,c_109264]) ).
tcf(c_113993,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,X0) = iPr_def_10 )
| ( unordered_pair(unordered_pair(first(regular(intersection(iPr_def_11,X0))),first(regular(intersection(iPr_def_11,X0)))),unordered_pair(first(regular(intersection(iPr_def_11,X0))),unordered_pair(second(regular(intersection(iPr_def_11,X0))),second(regular(intersection(iPr_def_11,X0)))))) = regular(intersection(iPr_def_11,X0)) ) ),
inference(light_normalisation,[status(thm)],[c_113873,c_4629]) ).
tcf(c_122129,plain,
! [X0: $i] :
( member(regular(intersection(iPr_def_11,X0)),X0)
| ( intersection(iPr_def_11,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_105766,c_109929]) ).
tcf(c_135816,plain,
! [X0: $i] :
( ( intersection(iPr_def_11,X0) = iPr_def_10 )
| ~ member(regular(intersection(iPr_def_11,X0)),iPr_def_11) ),
inference(superposition,[status(thm)],[c_113993,c_106907]) ).
tcf(c_137798,plain,
! [X0: $i] : intersection(iPr_def_11,X0) = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_122129,c_23013,c_135816]) ).
tcf(c_137801,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_105768,c_137798]) ).
tcf(c_137941,plain,
domain_of(iPr_def_10) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4631,c_137801]) ).
tcf(c_137942,plain,
iPr_def_10 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_137941,c_108390]) ).
tcf(c_137943,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_137942,c_105757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM058-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.56 % Computer : n011.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.57 % DateTime : Thu Sep 24 02:47:29 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.62
% 0.09/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.62
% 0.09/0.62 % Detected problem language: tptp
% 0.14/0.63 % Proving...
% 89.87/15.16 % SZS status Started for theBenchmark.p
% 89.87/15.16 % SZS status Unsatisfiable for theBenchmark.p
% 89.87/15.16
% 89.87/15.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 89.87/15.16
% 89.87/15.16 % ------ iProver source info
% 89.87/15.16
% 89.87/15.16 % git: date: 2026-07-19 20:42:38 +0200
% 89.87/15.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 89.87/15.16 % git: non_committed_changes: false
% 89.87/15.16
% 89.87/15.16 % ------ Parsing...% successful
% 89.87/15.16
% 89.87/15.16
% 89.87/15.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 89.87/15.16
% 89.87/15.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 89.87/15.16
% 89.87/15.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 89.87/15.16
% 89.87/15.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 89.87/15.16 % ------ Proving...
% 89.87/15.16 % ------ Problem Properties
% 89.87/15.16
% 89.87/15.16 %
% 89.87/15.16 % clauses 120
% 89.87/15.16 % conjectures 2
% 89.87/15.16 % EPR 16
% 89.87/15.16 % Horn 108
% 89.87/15.16 % unary 31
% 89.87/15.16 % binary 58
% 89.87/15.16 % lits 254
% 89.87/15.16 % lits eq 44
% 89.87/15.16 % fd_pure 0
% 89.87/15.16 % fd_pseudo 0
% 89.87/15.16 % fd_cond 5
% 89.87/15.16 % fd_pseudo_cond 10
% 89.87/15.16 % AC symbols 0
% 89.87/15.16
% 89.87/15.16 % ------ Schedule dynamic 5 is on
% 89.87/15.16
% 89.87/15.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 89.87/15.16
% 89.87/15.16
% 89.87/15.16 % ------
% 89.87/15.16 % Current options:
% 89.87/15.16 % ------
% 89.87/15.16
% 89.87/15.16
% 89.87/15.16 %
% 89.87/15.16
% 89.87/15.16 % ------ Proving...
% 89.87/15.16 % Proof_search_loop: time out after: 4011 full_loop iterations
% 89.87/15.16
% 89.87/15.16 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 89.87/15.16
% 89.87/15.16
% 89.87/15.16 % ------
% 89.87/15.16 % Current options:
% 89.87/15.16 % ------
% 89.87/15.16
% 89.87/15.16
% 89.87/15.16 %
% 89.87/15.16
% 89.87/15.16 % ------ Proving...
% 89.87/15.16 %
% 89.87/15.16
% 89.87/15.16 % SZS status Unsatisfiable for theBenchmark.p
% 89.87/15.16
% 89.87/15.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 89.87/15.17
% 89.87/15.17
%------------------------------------------------------------------------------