TSTP Solution File: SEU238+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 17:05:04 EDT 2023
% Result : Theorem 7.30s 1.63s
% Output : CNFRefutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 126 ( 13 unt; 0 def)
% Number of atoms : 453 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 589 ( 262 ~; 243 |; 54 &)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 180 ( 1 sgn; 95 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f26,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f43,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(f45,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f49,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f51,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(f53,axiom,
! [X0] :
( ordinal(X0)
=> ( being_limit_ordinal(X0)
<=> ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> in(succ(X1),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(f54,conjecture,
! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> succ(X1) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f55,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X1] :
( ordinal(X1)
=> succ(X1) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
inference(negated_conjecture,[],[f54]) ).
fof(f63,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f45]) ).
fof(f64,plain,
~ ! [X0] :
( ordinal(X0)
=> ( ~ ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ~ ( ! [X2] :
( ordinal(X2)
=> succ(X2) != X0 )
& ~ being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f55]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f86,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f91,plain,
! [X0] :
( ( ordinal(succ(X0))
& epsilon_connected(succ(X0))
& epsilon_transitive(succ(X0))
& ~ empty(succ(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f93,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f94,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f93]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( in(X0,X1)
<=> ordinal_subset(succ(X0),X1) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f103,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f104,plain,
! [X0] :
( ( being_limit_ordinal(X0)
<=> ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) ) )
| ~ ordinal(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
? [X0] :
( ( ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
| ( ! [X2] :
( succ(X2) != X0
| ~ ordinal(X2) )
& ~ being_limit_ordinal(X0) ) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f138,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1) )
& ( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1) ) )
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f141,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f142,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(rectify,[],[f141]) ).
fof(f143,plain,
! [X0] :
( ? [X1] :
( ~ in(succ(X1),X0)
& in(X1,X0)
& ordinal(X1) )
=> ( ~ in(succ(sK13(X0)),X0)
& in(sK13(X0),X0)
& ordinal(sK13(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( ~ in(succ(sK13(X0)),X0)
& in(sK13(X0),X0)
& ordinal(sK13(X0)) ) )
& ( ! [X2] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2) )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f142,f143]) ).
fof(f145,plain,
( ? [X0] :
( ( ( being_limit_ordinal(X0)
& ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
| ( ! [X2] :
( succ(X2) != X0
| ~ ordinal(X2) )
& ~ being_limit_ordinal(X0) ) )
& ordinal(X0) )
=> ( ( ( being_limit_ordinal(sK14)
& ? [X1] :
( succ(X1) = sK14
& ordinal(X1) ) )
| ( ! [X2] :
( succ(X2) != sK14
| ~ ordinal(X2) )
& ~ being_limit_ordinal(sK14) ) )
& ordinal(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f146,plain,
( ? [X1] :
( succ(X1) = sK14
& ordinal(X1) )
=> ( sK14 = succ(sK15)
& ordinal(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( ( ( being_limit_ordinal(sK14)
& sK14 = succ(sK15)
& ordinal(sK15) )
| ( ! [X2] :
( succ(X2) != sK14
| ~ ordinal(X2) )
& ~ being_limit_ordinal(sK14) ) )
& ordinal(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f105,f146,f145]) ).
fof(f148,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f162,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f163,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f178,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f180,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f215,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f216,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ~ subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f218,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f63]) ).
fof(f222,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f224,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f225,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(succ(X0),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f228,plain,
! [X2,X0] :
( in(succ(X2),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f229,plain,
! [X0] :
( being_limit_ordinal(X0)
| ordinal(sK13(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f230,plain,
! [X0] :
( being_limit_ordinal(X0)
| in(sK13(X0),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f231,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(succ(sK13(X0)),X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f232,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f147]) ).
fof(f233,plain,
( ordinal(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f147]) ).
fof(f235,plain,
( sK14 = succ(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f147]) ).
fof(f238,plain,
! [X2] :
( being_limit_ordinal(sK14)
| succ(X2) != sK14
| ~ ordinal(X2) ),
inference(cnf_transformation,[],[f147]) ).
fof(f245,plain,
! [X0] :
( ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f180,f162]) ).
fof(f247,plain,
! [X0] :
( epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f178,f162]) ).
fof(f250,plain,
! [X0,X1] :
( in(X0,X1)
| ~ ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f225,f162]) ).
fof(f251,plain,
! [X0,X1] :
( ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f224,f162]) ).
fof(f252,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f231,f162]) ).
fof(f253,plain,
! [X2,X0] :
( in(set_union2(X2,singleton(X2)),X0)
| ~ in(X2,X0)
| ~ ordinal(X2)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f228,f162]) ).
fof(f254,plain,
! [X2] :
( being_limit_ordinal(sK14)
| sK14 != set_union2(X2,singleton(X2))
| ~ ordinal(X2) ),
inference(definition_unfolding,[],[f238,f162]) ).
fof(f256,plain,
( sK14 = set_union2(sK15,singleton(sK15))
| ~ being_limit_ordinal(sK14) ),
inference(definition_unfolding,[],[f235,f162]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_61,plain,
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_75,plain,
( ~ ordinal(X0)
| ordinal(set_union2(X0,singleton(X0))) ),
inference(cnf_transformation,[],[f245]) ).
cnf(c_77,plain,
( ~ ordinal(X0)
| epsilon_transitive(set_union2(X0,singleton(X0))) ),
inference(cnf_transformation,[],[f247]) ).
cnf(c_113,plain,
( ~ subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_114,plain,
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_116,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f218]) ).
cnf(c_120,plain,
( ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| in(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_122,plain,
( ~ ordinal_subset(set_union2(X0,singleton(X0)),X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f250]) ).
cnf(c_123,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ordinal_subset(set_union2(X0,singleton(X0)),X1) ),
inference(cnf_transformation,[],[f251]) ).
cnf(c_126,plain,
( ~ in(set_union2(sK13(X0),singleton(sK13(X0))),X0)
| ~ ordinal(X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f252]) ).
cnf(c_127,plain,
( ~ ordinal(X0)
| in(sK13(X0),X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f230]) ).
cnf(c_128,plain,
( ~ ordinal(X0)
| ordinal(sK13(X0))
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_129,plain,
( ~ in(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| in(set_union2(X0,singleton(X0)),X1) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_130,negated_conjecture,
( set_union2(X0,singleton(X0)) != sK14
| ~ ordinal(X0)
| being_limit_ordinal(sK14) ),
inference(cnf_transformation,[],[f254]) ).
cnf(c_132,negated_conjecture,
( ~ being_limit_ordinal(sK14)
| set_union2(sK15,singleton(sK15)) = sK14 ),
inference(cnf_transformation,[],[f256]) ).
cnf(c_134,negated_conjecture,
( ~ being_limit_ordinal(sK14)
| ordinal(sK15) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_135,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f232]) ).
cnf(c_1133,plain,
( X0 != X1
| X1 != X2
| ~ ordinal(X0)
| ~ ordinal(X2)
| ordinal_subset(X0,X2) ),
inference(resolution_lifted,[status(thm)],[c_113,c_116]) ).
cnf(c_1134,plain,
( ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(unflattening,[status(thm)],[c_1133]) ).
cnf(c_1271,plain,
( ~ ordinal(X0)
| ordinal_subset(X0,X0) ),
inference(prop_impl_just,[status(thm)],[c_1134]) ).
cnf(c_2148,plain,
X0 = X0,
theory(equality) ).
cnf(c_2150,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2151,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_2156,plain,
( X0 != X1
| ~ ordinal_subset(X1,X2)
| ordinal_subset(X0,X2) ),
theory(equality) ).
cnf(c_2157,plain,
( X0 != X1
| X2 != X3
| ~ element(X1,X3)
| element(X0,X2) ),
theory(equality) ).
cnf(c_3096,plain,
( ~ ordinal(sK14)
| in(sK13(sK14),sK14)
| being_limit_ordinal(sK14) ),
inference(instantiation,[status(thm)],[c_127]) ).
cnf(c_3097,plain,
( ~ ordinal(sK14)
| ordinal(sK13(sK14))
| being_limit_ordinal(sK14) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_3123,plain,
( ~ ordinal_subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(sK14)
| subset(set_union2(X0,singleton(X0)),sK14) ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_3240,plain,
sK14 = sK14,
inference(instantiation,[status(thm)],[c_2148]) ).
cnf(c_3289,plain,
( X0 != X1
| sK14 != X2
| ~ in(X1,X2)
| in(X0,sK14) ),
inference(instantiation,[status(thm)],[c_2151]) ).
cnf(c_3684,plain,
( X0 != X1
| sK14 != sK14
| ~ in(X1,sK14)
| in(X0,sK14) ),
inference(instantiation,[status(thm)],[c_3289]) ).
cnf(c_3691,plain,
( ~ in(X0,sK14)
| ~ in(sK14,X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_5029,plain,
( X0 != set_union2(X1,singleton(X1))
| sK14 != sK14
| ~ in(set_union2(X1,singleton(X1)),sK14)
| in(X0,sK14) ),
inference(instantiation,[status(thm)],[c_3684]) ).
cnf(c_5990,plain,
( ~ subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(X0)
| proper_subset(set_union2(X0,singleton(X0)),sK14)
| being_limit_ordinal(sK14) ),
inference(resolution,[status(thm)],[c_61,c_130]) ).
cnf(c_7472,plain,
( ~ ordinal_subset(sK14,X0)
| ~ being_limit_ordinal(sK14)
| ordinal_subset(set_union2(sK15,singleton(sK15)),X0) ),
inference(resolution,[status(thm)],[c_2156,c_132]) ).
cnf(c_7632,plain,
( ~ ordinal_subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(set_union2(X0,singleton(X0)))
| ~ ordinal(X0)
| ~ ordinal(sK14)
| proper_subset(set_union2(X0,singleton(X0)),sK14)
| being_limit_ordinal(sK14) ),
inference(resolution,[status(thm)],[c_114,c_5990]) ).
cnf(c_7822,plain,
( ~ ordinal(X0)
| ~ ordinal_subset(set_union2(X0,singleton(X0)),sK14)
| proper_subset(set_union2(X0,singleton(X0)),sK14)
| being_limit_ordinal(sK14) ),
inference(global_subsumption_just,[status(thm)],[c_7632,c_135,c_75,c_3123,c_5990]) ).
cnf(c_7823,plain,
( ~ ordinal_subset(set_union2(X0,singleton(X0)),sK14)
| ~ ordinal(X0)
| proper_subset(set_union2(X0,singleton(X0)),sK14)
| being_limit_ordinal(sK14) ),
inference(renaming,[status(thm)],[c_7822]) ).
cnf(c_8254,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_2150,c_2148]) ).
cnf(c_8517,plain,
( ~ ordinal_subset(sK14,X0)
| ~ ordinal(X0)
| ~ ordinal(sK15)
| ~ being_limit_ordinal(sK14)
| in(sK15,X0) ),
inference(resolution,[status(thm)],[c_122,c_7472]) ).
cnf(c_8603,plain,
( ~ in(X0,sK14)
| ~ ordinal(X0)
| ~ ordinal(sK14)
| proper_subset(set_union2(X0,singleton(X0)),sK14)
| being_limit_ordinal(sK14) ),
inference(resolution,[status(thm)],[c_123,c_7823]) ).
cnf(c_8669,plain,
( X0 != X1
| ~ in(X1,sK14)
| ~ being_limit_ordinal(sK14)
| in(X0,set_union2(sK15,singleton(sK15))) ),
inference(resolution,[status(thm)],[c_2151,c_132]) ).
cnf(c_9000,plain,
( X0 != X1
| ~ element(X1,sK14)
| ~ being_limit_ordinal(sK14)
| element(X0,set_union2(sK15,singleton(sK15))) ),
inference(resolution,[status(thm)],[c_2157,c_132]) ).
cnf(c_10857,plain,
( ~ ordinal(X0)
| ~ ordinal_subset(sK14,X0)
| ~ being_limit_ordinal(sK14)
| in(sK15,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8517,c_134,c_8517]) ).
cnf(c_10858,plain,
( ~ ordinal_subset(sK14,X0)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK14)
| in(sK15,X0) ),
inference(renaming,[status(thm)],[c_10857]) ).
cnf(c_10884,plain,
( ~ ordinal(sK14)
| ~ being_limit_ordinal(sK14)
| in(sK15,sK14) ),
inference(resolution,[status(thm)],[c_10858,c_1271]) ).
cnf(c_11429,plain,
~ in(sK14,sK14),
inference(instantiation,[status(thm)],[c_3691]) ).
cnf(c_13919,plain,
( sK14 != set_union2(sK15,singleton(sK15))
| sK14 != sK14
| ~ in(set_union2(sK15,singleton(sK15)),sK14)
| in(sK14,sK14) ),
inference(instantiation,[status(thm)],[c_5029]) ).
cnf(c_14103,plain,
( ~ being_limit_ordinal(sK14)
| sK14 = set_union2(sK15,singleton(sK15)) ),
inference(resolution,[status(thm)],[c_8254,c_132]) ).
cnf(c_14650,plain,
( ~ in(set_union2(sK15,singleton(sK15)),sK14)
| ~ being_limit_ordinal(sK14)
| in(sK14,set_union2(sK15,singleton(sK15))) ),
inference(resolution,[status(thm)],[c_14103,c_8669]) ).
cnf(c_14651,plain,
( ~ element(set_union2(sK15,singleton(sK15)),sK14)
| ~ being_limit_ordinal(sK14)
| element(sK14,set_union2(sK15,singleton(sK15))) ),
inference(resolution,[status(thm)],[c_14103,c_9000]) ).
cnf(c_16563,plain,
( ~ being_limit_ordinal(sK14)
| ~ in(set_union2(sK15,singleton(sK15)),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_14650,c_3240,c_11429,c_13919,c_14103]) ).
cnf(c_16564,plain,
( ~ in(set_union2(sK15,singleton(sK15)),sK14)
| ~ being_limit_ordinal(sK14) ),
inference(renaming,[status(thm)],[c_16563]) ).
cnf(c_16573,plain,
( ~ in(sK15,sK14)
| ~ ordinal(sK14)
| ~ ordinal(sK15)
| ~ being_limit_ordinal(sK14) ),
inference(resolution,[status(thm)],[c_16564,c_129]) ).
cnf(c_16574,plain,
~ being_limit_ordinal(sK14),
inference(global_subsumption_just,[status(thm)],[c_14651,c_135,c_134,c_10884,c_16573]) ).
cnf(c_16584,plain,
( ~ in(X0,sK14)
| ~ ordinal(X0)
| ~ ordinal(sK14)
| proper_subset(set_union2(X0,singleton(X0)),sK14) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8603,c_16574]) ).
cnf(c_16888,plain,
( ~ ordinal(X0)
| ~ in(X0,sK14)
| proper_subset(set_union2(X0,singleton(X0)),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_16584,c_135,c_16584]) ).
cnf(c_16889,plain,
( ~ in(X0,sK14)
| ~ ordinal(X0)
| proper_subset(set_union2(X0,singleton(X0)),sK14) ),
inference(renaming,[status(thm)],[c_16888]) ).
cnf(c_16903,plain,
( ~ epsilon_transitive(set_union2(X0,singleton(X0)))
| ~ in(X0,sK14)
| ~ ordinal(X0)
| ~ ordinal(sK14)
| in(set_union2(X0,singleton(X0)),sK14) ),
inference(resolution,[status(thm)],[c_16889,c_120]) ).
cnf(c_20939,plain,
( ~ ordinal(X0)
| ~ in(X0,sK14)
| in(set_union2(X0,singleton(X0)),sK14) ),
inference(global_subsumption_just,[status(thm)],[c_16903,c_135,c_77,c_16903]) ).
cnf(c_20940,plain,
( ~ in(X0,sK14)
| ~ ordinal(X0)
| in(set_union2(X0,singleton(X0)),sK14) ),
inference(renaming,[status(thm)],[c_20939]) ).
cnf(c_20957,plain,
( ~ in(sK13(sK14),sK14)
| ~ ordinal(sK13(sK14))
| ~ ordinal(sK14)
| being_limit_ordinal(sK14) ),
inference(resolution,[status(thm)],[c_20940,c_126]) ).
cnf(c_20958,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20957,c_16574,c_3096,c_3097,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 12:56:46 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.30/1.63 % SZS status Started for theBenchmark.p
% 7.30/1.63 % SZS status Theorem for theBenchmark.p
% 7.30/1.63
% 7.30/1.63 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.30/1.63
% 7.30/1.63 ------ iProver source info
% 7.30/1.63
% 7.30/1.63 git: date: 2023-05-31 18:12:56 +0000
% 7.30/1.63 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.30/1.63 git: non_committed_changes: false
% 7.30/1.63 git: last_make_outside_of_git: false
% 7.30/1.63
% 7.30/1.63 ------ Parsing...
% 7.30/1.63 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.30/1.63
% 7.30/1.63 ------ Preprocessing... sup_sim: 0 sf_s rm: 21 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 7.30/1.63
% 7.30/1.63 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.30/1.63
% 7.30/1.63 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.30/1.63 ------ Proving...
% 7.30/1.63 ------ Problem Properties
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63 clauses 60
% 7.30/1.63 conjectures 6
% 7.30/1.63 EPR 38
% 7.30/1.63 Horn 55
% 7.30/1.63 unary 25
% 7.30/1.63 binary 17
% 7.30/1.63 lits 121
% 7.30/1.63 lits eq 11
% 7.30/1.63 fd_pure 0
% 7.30/1.63 fd_pseudo 0
% 7.30/1.63 fd_cond 1
% 7.30/1.63 fd_pseudo_cond 2
% 7.30/1.63 AC symbols 0
% 7.30/1.63
% 7.30/1.63 ------ Input Options Time Limit: Unbounded
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63 ------
% 7.30/1.63 Current options:
% 7.30/1.63 ------
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63 ------ Proving...
% 7.30/1.63
% 7.30/1.63
% 7.30/1.63 % SZS status Theorem for theBenchmark.p
% 7.30/1.63
% 7.30/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.30/1.63
% 7.30/1.64
%------------------------------------------------------------------------------