TSTP Solution File: NUM401+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 11:30:17 EDT 2023
% Result : Theorem 3.81s 1.18s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 128 ( 16 unt; 0 def)
% Number of atoms : 489 ( 75 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 562 ( 201 ~; 236 |; 95 &)
% ( 12 <=>; 17 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 189 ( 4 sgn; 139 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f11,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f13,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f19,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f39,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f40,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(f46,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f48,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,succ(X1))
<=> ordinal_subset(X0,X1) ) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f61,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f66,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f61]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f69,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f76,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f77,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f84,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f87,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f86]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
? [X0] :
( ? [X1] :
( ( in(X0,succ(X1))
<~> ordinal_subset(X0,X1) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f100,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f101,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f103,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f103,f104]) ).
fof(f106,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f107,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f106]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK1(X0),X0)
& in(sK1(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK1(X0),X0)
& in(sK1(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f107,f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f112,f113]) ).
fof(f143,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f85]) ).
fof(f144,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(nnf_transformation,[],[f93]) ).
fof(f145,plain,
? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
( ? [X0] :
( ? [X1] :
( ( ~ ordinal_subset(X0,X1)
| ~ in(X0,succ(X1)) )
& ( ordinal_subset(X0,X1)
| in(X0,succ(X1)) )
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ( ~ ordinal_subset(sK17,X1)
| ~ in(sK17,succ(X1)) )
& ( ordinal_subset(sK17,X1)
| in(sK17,succ(X1)) )
& ordinal(X1) )
& ordinal(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( ? [X1] :
( ( ~ ordinal_subset(sK17,X1)
| ~ in(sK17,succ(X1)) )
& ( ordinal_subset(sK17,X1)
| in(sK17,succ(X1)) )
& ordinal(X1) )
=> ( ( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,succ(sK18)) )
& ( ordinal_subset(sK17,sK18)
| in(sK17,succ(sK18)) )
& ordinal(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
( ( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,succ(sK18)) )
& ( ordinal_subset(sK17,sK18)
| in(sK17,succ(sK18)) )
& ordinal(sK18)
& ordinal(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f145,f147,f146]) ).
fof(f150,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f162,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f165,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f166,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f167,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f168,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f171,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f114]) ).
fof(f175,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f114]) ).
fof(f176,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f114]) ).
fof(f190,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f232,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f234,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f240,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f242,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f148]) ).
fof(f243,plain,
ordinal(sK18),
inference(cnf_transformation,[],[f148]) ).
fof(f244,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,succ(sK18)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f245,plain,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,succ(sK18)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f260,plain,
( ~ ordinal_subset(sK17,sK18)
| ~ in(sK17,set_union2(sK18,singleton(sK18))) ),
inference(definition_unfolding,[],[f245,f166]) ).
fof(f261,plain,
( ordinal_subset(sK17,sK18)
| in(sK17,set_union2(sK18,singleton(sK18))) ),
inference(definition_unfolding,[],[f244,f166]) ).
fof(f264,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f168]) ).
fof(f265,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f264]) ).
fof(f266,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f167]) ).
fof(f267,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f176]) ).
fof(f268,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f175]) ).
fof(f269,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f174]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_52,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_59,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_60,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_65,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f265]) ).
cnf(c_66,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f266]) ).
cnf(c_69,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_73,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f267]) ).
cnf(c_74,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f268]) ).
cnf(c_75,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f269]) ).
cnf(c_81,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f190]) ).
cnf(c_129,plain,
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
cnf(c_130,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X1,X1) ),
inference(cnf_transformation,[],[f234]) ).
cnf(c_136,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_138,negated_conjecture,
( ~ in(sK17,set_union2(sK18,singleton(sK18)))
| ~ ordinal_subset(sK17,sK18) ),
inference(cnf_transformation,[],[f260]) ).
cnf(c_139,negated_conjecture,
( in(sK17,set_union2(sK18,singleton(sK18)))
| ordinal_subset(sK17,sK18) ),
inference(cnf_transformation,[],[f261]) ).
cnf(c_140,negated_conjecture,
ordinal(sK18),
inference(cnf_transformation,[],[f243]) ).
cnf(c_141,negated_conjecture,
ordinal(sK17),
inference(cnf_transformation,[],[f242]) ).
cnf(c_1946,plain,
( ordinal_subset(X0,X0)
| ~ ordinal(X0)
| ~ sP0_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_split])],[c_130]) ).
cnf(c_1947,plain,
( ~ ordinal(X0)
| ~ sP1_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_split])],[c_130]) ).
cnf(c_1948,plain,
( sP0_iProver_split
| sP1_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_130]) ).
cnf(c_1964,plain,
( ~ ordinal(empty_set)
| ~ sP1_iProver_split ),
inference(instantiation,[status(thm)],[c_1947]) ).
cnf(c_2977,plain,
epsilon_transitive(sK18),
inference(superposition,[status(thm)],[c_140,c_52]) ).
cnf(c_2978,plain,
epsilon_transitive(sK17),
inference(superposition,[status(thm)],[c_141,c_52]) ).
cnf(c_3142,plain,
( ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1946,c_81,c_1946,c_1964,c_1948]) ).
cnf(c_3178,plain,
( ~ in(sK17,singleton(sK18))
| ~ ordinal_subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_73,c_138]) ).
cnf(c_3205,plain,
( ~ in(sK17,sK18)
| ~ ordinal_subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_74,c_138]) ).
cnf(c_3364,plain,
( ~ in(sK17,sK18)
| ~ ordinal(sK17)
| ~ ordinal(sK18)
| ordinal_subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_59,c_3205]) ).
cnf(c_3368,plain,
( ~ in(sK17,sK18)
| ordinal_subset(sK18,sK17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3364,c_140,c_141]) ).
cnf(c_3407,plain,
( in(sK17,singleton(sK18))
| in(sK17,sK18)
| ordinal_subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_139,c_75]) ).
cnf(c_3471,plain,
( sK17 = sK18
| in(sK17,sK18)
| ordinal_subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_3407,c_66]) ).
cnf(c_3614,plain,
( ~ ordinal(sK17)
| ~ ordinal(sK18)
| sK17 = sK18
| in(sK17,sK18)
| subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_3471,c_129]) ).
cnf(c_3624,plain,
( sK17 = sK18
| in(sK17,sK18)
| subset(sK17,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3614,c_140,c_141]) ).
cnf(c_3754,plain,
( ~ ordinal(sK17)
| ~ ordinal(sK18)
| sK17 = sK18
| in(sK18,sK17)
| ordinal_subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_136,c_3368]) ).
cnf(c_3778,plain,
( sK17 = sK18
| in(sK18,sK17)
| ordinal_subset(sK18,sK17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3754,c_140,c_141]) ).
cnf(c_3948,plain,
( ~ subset(sK18,sK17)
| sK17 = sK18
| in(sK17,sK18) ),
inference(superposition,[status(thm)],[c_3624,c_60]) ).
cnf(c_3958,plain,
( ~ ordinal(sK17)
| ~ ordinal(sK18)
| sK17 = sK18
| in(sK18,sK17)
| subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_3778,c_129]) ).
cnf(c_3959,plain,
( sK17 = sK18
| in(sK18,sK17)
| subset(sK18,sK17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3958,c_140,c_141]) ).
cnf(c_3970,plain,
( ~ subset(sK17,sK18)
| sK17 = sK18
| in(sK18,sK17) ),
inference(superposition,[status(thm)],[c_3959,c_60]) ).
cnf(c_4472,plain,
( sK17 = sK18
| in(sK17,sK18)
| in(sK18,sK17) ),
inference(superposition,[status(thm)],[c_3959,c_3948]) ).
cnf(c_4490,plain,
( ~ epsilon_transitive(sK18)
| sK17 = sK18
| in(sK18,sK17)
| subset(sK17,sK18) ),
inference(superposition,[status(thm)],[c_4472,c_69]) ).
cnf(c_4501,plain,
( sK17 = sK18
| in(sK18,sK17)
| subset(sK17,sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4490,c_2977]) ).
cnf(c_4505,plain,
( in(sK18,sK17)
| sK17 = sK18 ),
inference(global_subsumption_just,[status(thm)],[c_4501,c_3970,c_4501]) ).
cnf(c_4506,plain,
( sK17 = sK18
| in(sK18,sK17) ),
inference(renaming,[status(thm)],[c_4505]) ).
cnf(c_4511,plain,
( ~ epsilon_transitive(sK17)
| sK17 = sK18
| subset(sK18,sK17) ),
inference(superposition,[status(thm)],[c_4506,c_69]) ).
cnf(c_4513,plain,
( ~ in(sK17,sK18)
| sK17 = sK18 ),
inference(superposition,[status(thm)],[c_4506,c_49]) ).
cnf(c_4521,plain,
( sK17 = sK18
| subset(sK18,sK17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4511,c_2978]) ).
cnf(c_4524,plain,
sK17 = sK18,
inference(global_subsumption_just,[status(thm)],[c_4521,c_3948,c_4521,c_4513]) ).
cnf(c_4541,plain,
( ~ in(sK18,singleton(sK18))
| ~ ordinal_subset(sK18,sK18) ),
inference(demodulation,[status(thm)],[c_3178,c_4524]) ).
cnf(c_4554,plain,
~ ordinal_subset(sK18,sK18),
inference(forward_subsumption_resolution,[status(thm)],[c_4541,c_65]) ).
cnf(c_4620,plain,
~ ordinal(sK18),
inference(superposition,[status(thm)],[c_3142,c_4554]) ).
cnf(c_4621,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4620,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 15:34:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.81/1.18 % SZS status Started for theBenchmark.p
% 3.81/1.18 % SZS status Theorem for theBenchmark.p
% 3.81/1.18
% 3.81/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.81/1.18
% 3.81/1.18 ------ iProver source info
% 3.81/1.18
% 3.81/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.81/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.81/1.18 git: non_committed_changes: false
% 3.81/1.18 git: last_make_outside_of_git: false
% 3.81/1.18
% 3.81/1.18 ------ Parsing...
% 3.81/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.81/1.18
% 3.81/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 23 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 3.81/1.18
% 3.81/1.18 ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.81/1.18
% 3.81/1.18 ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/1.18 ------ Proving...
% 3.81/1.18 ------ Problem Properties
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18 clauses 66
% 3.81/1.18 conjectures 4
% 3.81/1.18 EPR 39
% 3.81/1.18 Horn 57
% 3.81/1.18 unary 27
% 3.81/1.18 binary 22
% 3.81/1.18 lits 128
% 3.81/1.18 lits eq 16
% 3.81/1.18 fd_pure 0
% 3.81/1.18 fd_pseudo 0
% 3.81/1.18 fd_cond 1
% 3.81/1.18 fd_pseudo_cond 8
% 3.81/1.18 AC symbols 0
% 3.81/1.18
% 3.81/1.18 ------ Schedule dynamic 5 is on
% 3.81/1.18
% 3.81/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18 ------
% 3.81/1.18 Current options:
% 3.81/1.18 ------
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18 ------ Proving...
% 3.81/1.18
% 3.81/1.18
% 3.81/1.18 % SZS status Theorem for theBenchmark.p
% 3.81/1.18
% 3.81/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/1.18
% 3.81/1.19
%------------------------------------------------------------------------------