%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET473-6 : 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 : n016.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 02:47:18 PM UTC 2026
% Result : Unsatisfiable 32.78s 5.35s
% Output : CNFRefutation 32.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of formulae : 125 ( 40 unt; 3 def)
% Number of atoms : 301 ( 112 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 184 ( 76 ~; 108 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 185 ( 0 sgn 185 !; 0 ?; 126 :)
% 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(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(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(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(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(f69,axiom,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
file('/export/starexec/sandbox/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,
y = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_1) ).
fof(f123,plain,
null_class = y,
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
domain_of(restrict(x,y,y)) != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_2) ).
fof(f125,plain,
y != domain_of(restrict(x,y,y)),
inference(reorient_equations,[],[f124]) ).
fof(f130,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(f139,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,f130]) ).
fof(f142,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,f130]) ).
fof(f145,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| y != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) ),
inference(definition_unfolding,[],[f30,f28,f12,f123]) ).
fof(f166,plain,
! [X0] :
( member(regular(X0),X0)
| y = X0 ),
inference(definition_unfolding,[],[f68,f123]) ).
fof(f167,plain,
! [X0] :
( intersection(X0,regular(X0)) = y
| y = X0 ),
inference(definition_unfolding,[],[f70,f123,f123]) ).
fof(f191,plain,
y != domain_of(intersection(x,cross_product(y,y))),
inference(definition_unfolding,[],[f125,f28]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_166,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_174,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,[],[f139]) ).
tcf(c_177,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,[],[f142]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(cnf_transformation,[],[f145]) ).
tcf(c_187,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != y ) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_215,negated_conjecture,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = y ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_216,negated_conjecture,
! [X0: $i] :
( ( X0 = y )
| ( intersection(X0,regular(X0)) = y ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_256,negated_conjecture,
domain_of(intersection(x,cross_product(y,y))) != y,
inference(cnf_transformation,[],[f191]) ).
tcf(c_2975,definition,
iPr_def_10 = cross_product(y,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2976,definition,
iPr_def_11 = intersection(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2977,definition,
iPr_def_12 = domain_of(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2979,negated_conjecture,
iPr_def_12 != y,
inference(demodulation,[status(thm)],[c_256,c_2975,c_2976,c_2977]) ).
tcf(c_2981,negated_conjecture,
! [X0: $i] :
( ( X0 = y )
| ( intersection(X0,regular(X0)) = y ) ),
inference(demodulation,[status(thm)],[c_216]) ).
tcf(c_2982,negated_conjecture,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = y ) ),
inference(demodulation,[status(thm)],[c_215]) ).
tcf(c_2984,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ member(X1,domain_of(X0))
| ( intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)) != y ) ),
inference(demodulation,[status(thm)],[c_187]) ).
tcf(c_4006,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_164,c_181]) ).
tcf(c_4007,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = y ) ),
inference(superposition,[status(thm)],[c_2982,c_181]) ).
tcf(c_4033,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = y ) ),
inference(superposition,[status(thm)],[c_2982,c_182]) ).
tcf(c_4035,plain,
! [X0: $i,X1: $i] :
( member(X0,regular(X1))
| ( X1 = y )
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_2981,c_182]) ).
tcf(c_4036,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_2976,c_182]) ).
tcf(c_4071,plain,
( member(regular(iPr_def_11),iPr_def_10)
| ( y = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2982,c_4036]) ).
tcf(c_4114,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(intersection(X0,X1),X2)),X1)
| ( intersection(intersection(X0,X1),X2) = y ) ),
inference(superposition,[status(thm)],[c_4007,c_182]) ).
tcf(c_4115,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(regular(intersection(intersection(X0,X1),X2)),X0)
| ( intersection(intersection(X0,X1),X2) = y ) ),
inference(superposition,[status(thm)],[c_4007,c_181]) ).
tcf(c_4205,plain,
! [X0: $i] :
( ( complement(X0) = y )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_2982,c_184]) ).
tcf(c_4524,plain,
! [X0: $i,X1: $i] : subclass(intersection(X0,X1),X0),
inference(superposition,[status(thm)],[c_4006,c_165]) ).
tcf(c_4610,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_166,c_163]) ).
tcf(c_4781,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = intersection(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2975,c_186]) ).
tcf(c_4879,plain,
! [X0: $i] :
( subclass(y,X0)
| ( X0 = y ) ),
inference(superposition,[status(thm)],[c_2981,c_4524]) ).
tcf(c_4920,plain,
! [X0: $i] :
( member(regular(X0),universal_class)
| ( X0 = y ) ),
inference(superposition,[status(thm)],[c_2982,c_4610]) ).
tcf(c_4933,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ( X1 = y )
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_4035,c_4610]) ).
tcf(c_5012,plain,
! [X0: $i] :
( ( X0 = y )
| ~ subclass(X0,y) ),
inference(superposition,[status(thm)],[c_4879,c_169]) ).
tcf(c_5027,plain,
complement(universal_class) = y,
inference(superposition,[status(thm)],[c_4920,c_4205]) ).
tcf(c_5177,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ( X1 = y )
| ~ member(X0,X1)
| ~ member(X0,regular(X1)) ),
inference(superposition,[status(thm)],[c_2981,c_183]) ).
tcf(c_5256,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_5027,c_184]) ).
tcf(c_5318,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,regular(X1))
| ~ member(X0,X1)
| ( X1 = y ) ),
inference(global_subsumption_just,[status(thm)],[c_5177,c_4610,c_5177,c_5256]) ).
tcf(c_5319,plain,
! [X0: $i,X1: $i] :
( ( X1 = y )
| ~ member(X0,X1)
| ~ member(X0,regular(X1)) ),
inference(renaming,[status(thm)],[c_5318]) ).
tcf(c_6243,plain,
! [X0: $i] :
( member(regular(intersection(iPr_def_10,X0)),iPr_def_10)
| ( intersection(X0,iPr_def_10) = y ) ),
inference(superposition,[status(thm)],[c_4781,c_4033]) ).
tcf(c_6244,plain,
! [X0: $i] :
( member(regular(intersection(iPr_def_10,X0)),X0)
| ( intersection(X0,iPr_def_10) = y ) ),
inference(superposition,[status(thm)],[c_4781,c_4007]) ).
tcf(c_6338,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = y ) ),
inference(superposition,[status(thm)],[c_2982,c_181]) ).
tcf(c_6340,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ( X1 = y )
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_2981,c_181]) ).
tcf(c_6893,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,y)
| ( X1 = y ) ),
inference(global_subsumption_just,[status(thm)],[c_6340,c_4933,c_5256]) ).
tcf(c_6894,plain,
! [X0: $i,X1: $i] :
( ( X1 = y )
| ~ member(X0,y) ),
inference(renaming,[status(thm)],[c_6893]) ).
tcf(c_6914,plain,
! [X0: $i,X1: $i] :
( ( X1 = y )
| ( intersection(y,X0) = y ) ),
inference(superposition,[status(thm)],[c_6338,c_6894]) ).
tcf(c_7266,plain,
! [X0: $i] : intersection(y,X0) = y,
inference(superposition,[status(thm)],[c_4524,c_5012]) ).
tcf(c_7330,plain,
! [X0: $i] : intersection(y,X0) = y,
inference(global_subsumption_just,[status(thm)],[c_6914,c_7266]) ).
tcf(c_7334,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| ~ member(X0,y) ),
inference(superposition,[status(thm)],[c_7330,c_182]) ).
tcf(c_7336,plain,
! [X0: $i] : ~ member(X0,domain_of(y)),
inference(superposition,[status(thm)],[c_7330,c_2984]) ).
tcf(c_7370,plain,
! [X0: $i] : ~ member(X0,y),
inference(global_subsumption_just,[status(thm)],[c_4933,c_4610,c_5256,c_7334]) ).
tcf(c_7541,plain,
! [X0: $i] : ~ member(X0,domain_of(y)),
inference(superposition,[status(thm)],[c_7266,c_2984]) ).
tcf(c_7552,plain,
domain_of(y) = y,
inference(superposition,[status(thm)],[c_2982,c_7541]) ).
tcf(c_8192,plain,
domain_of(y) = y,
inference(superposition,[status(thm)],[c_2982,c_7336]) ).
tcf(c_8196,plain,
! [X0: $i] : ~ member(X0,y),
inference(demodulation,[status(thm)],[c_7336,c_8192]) ).
tcf(c_15791,plain,
( member(regular(y),iPr_def_10)
| ( y = iPr_def_10 )
| ( intersection(regular(iPr_def_10),iPr_def_10) = y ) ),
inference(superposition,[status(thm)],[c_2981,c_6243]) ).
tcf(c_15942,plain,
( member(regular(y),iPr_def_10)
| ( y = iPr_def_10 )
| ( intersection(iPr_def_10,regular(iPr_def_10)) = y ) ),
inference(demodulation,[status(thm)],[c_15791,c_4781]) ).
tcf(c_15962,plain,
( member(regular(y),regular(iPr_def_10))
| ( y = iPr_def_10 )
| ( intersection(regular(iPr_def_10),iPr_def_10) = y ) ),
inference(superposition,[status(thm)],[c_2981,c_6244]) ).
tcf(c_16141,plain,
( member(regular(y),regular(iPr_def_10))
| ( y = iPr_def_10 )
| ( intersection(iPr_def_10,regular(iPr_def_10)) = y ) ),
inference(demodulation,[status(thm)],[c_15962,c_4781]) ).
tcf(c_16152,plain,
( ( y = iPr_def_10 )
| ( intersection(iPr_def_10,regular(iPr_def_10)) = y )
| ~ member(regular(y),iPr_def_10) ),
inference(superposition,[status(thm)],[c_16141,c_5319]) ).
tcf(c_23501,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(y,X1)),regular(X0))
| ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y ) ),
inference(superposition,[status(thm)],[c_2981,c_4114]) ).
tcf(c_24124,plain,
! [X0: $i,X1: $i] :
( member(regular(y),regular(X0))
| ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y ) ),
inference(demodulation,[status(thm)],[c_23501,c_7266]) ).
tcf(c_24143,plain,
! [X0: $i,X1: $i] :
( ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y )
| ~ member(regular(y),X0) ),
inference(superposition,[status(thm)],[c_24124,c_5319]) ).
tcf(c_24221,plain,
! [X0: $i,X1: $i] :
( member(regular(intersection(y,X1)),X0)
| ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y ) ),
inference(superposition,[status(thm)],[c_2981,c_4115]) ).
tcf(c_24724,plain,
! [X0: $i,X1: $i] :
( member(regular(y),X0)
| ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y ) ),
inference(demodulation,[status(thm)],[c_24221,c_7266]) ).
tcf(c_39238,plain,
( ( y = iPr_def_10 )
| ( intersection(iPr_def_10,regular(iPr_def_10)) = y ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16152,c_15942]) ).
tcf(c_50084,plain,
! [X0: $i,X1: $i] :
( member(X0,y)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2975,c_174]) ).
tcf(c_50085,plain,
! [X0: $i,X1: $i] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_50084,c_8196]) ).
tcf(c_50733,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = y )
| ( unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))) = regular(cross_product(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2982,c_177]) ).
tcf(c_51080,plain,
! [X0: $i,X1: $i] :
( ( cross_product(X0,X1) = y )
| ~ member(regular(cross_product(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50733,c_50085]) ).
tcf(c_53905,plain,
( ( cross_product(y,y) = y )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2975,c_51080]) ).
tcf(c_53906,plain,
( ( y = iPr_def_10 )
| ~ member(regular(iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_53905,c_2975]) ).
tcf(c_74961,plain,
! [X0: $i,X1: $i] :
( ( X0 = y )
| ( intersection(intersection(X0,regular(X0)),X1) = y ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24143,c_24724]) ).
tcf(c_75035,plain,
! [X0: $i,X1: $i] :
( ( X1 = y )
| ~ member(X0,domain_of(intersection(X1,regular(X1)))) ),
inference(superposition,[status(thm)],[c_74961,c_2984]) ).
tcf(c_75985,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = y )
| ( intersection(intersection(X0,domain_of(intersection(X1,regular(X1)))),X2) = y ) ),
inference(superposition,[status(thm)],[c_4114,c_75035]) ).
tcf(c_85812,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = y )
| ~ member(X0,domain_of(intersection(X1,domain_of(intersection(X2,regular(X2)))))) ),
inference(superposition,[status(thm)],[c_75985,c_2984]) ).
tcf(c_86478,plain,
y = iPr_def_10,
inference(superposition,[status(thm)],[c_2982,c_53906]) ).
tcf(c_87770,plain,
! [X0: $i,X1: $i] :
( ( y = iPr_def_10 )
| ~ member(X0,domain_of(intersection(X1,domain_of(y)))) ),
inference(superposition,[status(thm)],[c_39238,c_85812]) ).
tcf(c_87794,plain,
! [X0: $i,X1: $i] :
( ( y = iPr_def_10 )
| ~ member(X0,domain_of(intersection(X1,y))) ),
inference(light_normalisation,[status(thm)],[c_87770,c_7552]) ).
tcf(c_88526,plain,
y = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_87794,c_86478]) ).
tcf(c_88945,plain,
domain_of(iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_7552,c_88526]) ).
tcf(c_88949,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_7370,c_88526]) ).
tcf(c_88990,plain,
( member(regular(iPr_def_11),iPr_def_10)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_4071,c_88526]) ).
tcf(c_89009,plain,
iPr_def_10 != iPr_def_12,
inference(demodulation,[status(thm)],[c_2979,c_88526]) ).
tcf(c_89014,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_88990,c_88949]) ).
tcf(c_89944,plain,
domain_of(iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2977,c_89014]) ).
tcf(c_91363,plain,
iPr_def_10 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_89944,c_88945]) ).
tcf(c_91364,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_91363,c_89009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET473-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:07:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 32.78/5.35 % SZS status Started for theBenchmark.p
% 32.78/5.35 % SZS status Unsatisfiable for theBenchmark.p
% 32.78/5.35
% 32.78/5.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.78/5.35
% 32.78/5.35 % ------ iProver source info
% 32.78/5.35
% 32.78/5.35 % git: date: 2026-07-19 20:42:38 +0200
% 32.78/5.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.78/5.35 % git: non_committed_changes: false
% 32.78/5.35
% 32.78/5.35 % ------ Parsing...% successful
% 32.78/5.35
% 32.78/5.35
% 32.78/5.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.78/5.35
% 32.78/5.35 % ------ 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 %
% 32.78/5.35
% 32.78/5.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.78/5.35
% 32.78/5.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.78/5.35 % ------ Proving...
% 32.78/5.35 % ------ Problem Properties
% 32.78/5.35
% 32.78/5.35 %
% 32.78/5.35 % clauses 85
% 32.78/5.35 % conjectures 6
% 32.78/5.35 % EPR 13
% 32.78/5.35 % Horn 77
% 32.78/5.35 % unary 24
% 32.78/5.35 % binary 40
% 32.78/5.35 % lits 173
% 32.78/5.35 % lits eq 29
% 32.78/5.35 % fd_pure 0
% 32.78/5.35 % fd_pseudo 0
% 32.78/5.35 % fd_cond 3
% 32.78/5.35 % fd_pseudo_cond 7
% 32.78/5.35 % AC symbols 0
% 32.78/5.35
% 32.78/5.35 % ------ Schedule dynamic 5 is on
% 32.78/5.35
% 32.78/5.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.78/5.35
% 32.78/5.35
% 32.78/5.35 % ------
% 32.78/5.35 % Current options:
% 32.78/5.35 % ------
% 32.78/5.35
% 32.78/5.35
% 32.78/5.35 %
% 32.78/5.35
% 32.78/5.35 % ------ Proving...
% 32.78/5.35 %
% 32.78/5.35
% 32.78/5.35 % SZS status Unsatisfiable for theBenchmark.p
% 32.78/5.35
% 32.78/5.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.78/5.35
% 32.78/5.35
%------------------------------------------------------------------------------