TSTP Solution File: NUM397+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 11:30:16 EDT 2023
% Result : Theorem 39.02s 6.20s
% Output : CNFRefutation 39.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 143 ( 12 unt; 0 def)
% Number of atoms : 483 ( 47 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 554 ( 214 ~; 224 |; 92 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 218 ( 2 sgn; 135 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f10,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f12,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f16,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(f17,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f35,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(f36,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f37,conjecture,
! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_ordinal1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ordinal(union(X0)) ),
inference(negated_conjecture,[],[f37]) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f49,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,[],[f16]) ).
fof(f52,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,[],[f49]) ).
fof(f67,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f74,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f75,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
? [X0] :
( ~ ordinal(union(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f81,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f82,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f87,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f88,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,[],[f67]) ).
fof(f89,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f89,f90]) ).
fof(f92,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) )
| ~ epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f93,plain,
! [X0] :
( ( epsilon_connected(X0)
| ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
=> ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0] :
( ( epsilon_connected(X0)
| ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) ) )
& ( ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) )
| ~ epsilon_connected(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f93,f94]) ).
fof(f96,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f97,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f99,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) )
| ~ in(sK3(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK3(X0,X1),X4) )
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK3(X0,X1),X4) )
=> ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK3(X0,X1),X3) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK4(X0,X1),X0)
& in(sK3(X0,X1),sK4(X0,X1)) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK5(X0,X5),X0)
& in(X5,sK5(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f99,f102,f101,f100]) ).
fof(f131,plain,
( ? [X0] :
( ~ ordinal(union(X0))
& ordinal(X0) )
=> ( ~ ordinal(union(sK19))
& ordinal(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ~ ordinal(union(sK19))
& ordinal(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f80,f131]) ).
fof(f133,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f146,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f147,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
! [X0] :
( epsilon_connected(X0)
| sK1(X0) != sK2(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
! [X0,X1,X5] :
( in(X5,sK5(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
! [X0,X1,X5] :
( in(sK5(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
! [X0,X1] :
( union(X0) = X1
| in(sK4(X0,X1),X0)
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f173,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f52]) ).
fof(f174,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f208,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f209,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f210,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f211,plain,
ordinal(sK19),
inference(cnf_transformation,[],[f132]) ).
fof(f212,plain,
~ ordinal(union(sK19)),
inference(cnf_transformation,[],[f132]) ).
fof(f214,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f215,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f218,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f220,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f222,plain,
! [X0,X5] :
( in(sK5(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f159]) ).
fof(f223,plain,
! [X0,X5] :
( in(X5,sK5(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f158]) ).
cnf(c_59,plain,
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_60,plain,
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_62,plain,
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_63,plain,
( sK2(X0) != sK1(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_64,plain,
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_65,plain,
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_66,plain,
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_68,plain,
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_70,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_72,plain,
( union(X0) = X1
| in(sK3(X0,X1),X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_75,plain,
( ~ in(X0,union(X1))
| in(sK5(X1,X0),X1) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_76,plain,
( ~ in(X0,union(X1))
| in(X0,sK5(X1,X0)) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_81,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f173]) ).
cnf(c_88,plain,
empty(empty_set),
inference(cnf_transformation,[],[f174]) ).
cnf(c_121,plain,
( ~ in(X0,X1)
| ~ ordinal(X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_122,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_123,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_124,negated_conjecture,
~ ordinal(union(sK19)),
inference(cnf_transformation,[],[f212]) ).
cnf(c_125,negated_conjecture,
ordinal(sK19),
inference(cnf_transformation,[],[f211]) ).
cnf(c_126,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_128,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_131,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_133,plain,
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_151,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_126]) ).
cnf(c_331,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_128,c_151]) ).
cnf(c_2609,plain,
X0 = X0,
theory(equality) ).
cnf(c_2611,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2615,plain,
( X0 != X1
| ~ ordinal(X1)
| ordinal(X0) ),
theory(equality) ).
cnf(c_3584,plain,
( ~ epsilon_connected(union(sK19))
| ~ epsilon_transitive(union(sK19))
| ordinal(union(sK19)) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_3585,plain,
( union(sK19) != X0
| ~ ordinal(X0)
| ordinal(union(sK19)) ),
inference(instantiation,[status(thm)],[c_2615]) ).
cnf(c_3586,plain,
( union(sK19) != empty_set
| ~ ordinal(empty_set)
| ordinal(union(sK19)) ),
inference(instantiation,[status(thm)],[c_3585]) ).
cnf(c_3607,plain,
( in(sK0(union(sK19)),union(sK19))
| epsilon_transitive(union(sK19)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_3608,plain,
( ~ subset(sK0(union(sK19)),union(sK19))
| epsilon_transitive(union(sK19)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_3617,plain,
( union(sK19) = X0
| in(sK3(sK19,X0),X0)
| in(sK4(sK19,X0),sK19) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_3618,plain,
( union(sK19) = empty_set
| in(sK3(sK19,empty_set),empty_set)
| in(sK4(sK19,empty_set),sK19) ),
inference(instantiation,[status(thm)],[c_3617]) ).
cnf(c_3662,plain,
( in(sK1(union(sK19)),union(sK19))
| epsilon_connected(union(sK19)) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_3663,plain,
( in(sK2(union(sK19)),union(sK19))
| epsilon_connected(union(sK19)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_3664,plain,
( sK2(union(sK19)) != sK1(union(sK19))
| epsilon_connected(union(sK19)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_3714,plain,
( ~ in(sK3(sK19,X0),X0)
| ~ empty(X0) ),
inference(instantiation,[status(thm)],[c_131]) ).
cnf(c_3719,plain,
( ~ in(sK3(sK19,empty_set),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_3714]) ).
cnf(c_3795,plain,
( ~ in(sK4(sK19,X0),sK19)
| ~ empty(sK19) ),
inference(instantiation,[status(thm)],[c_131]) ).
cnf(c_3800,plain,
( ~ in(sK4(sK19,empty_set),sK19)
| ~ empty(sK19) ),
inference(instantiation,[status(thm)],[c_3795]) ).
cnf(c_3937,plain,
( ~ in(sK0(union(sK19)),union(sK19))
| in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_4260,plain,
( ~ element(X0,sK19)
| in(X0,sK19)
| empty(sK19) ),
inference(instantiation,[status(thm)],[c_123]) ).
cnf(c_4481,plain,
epsilon_transitive(sK19),
inference(superposition,[status(thm)],[c_125,c_70]) ).
cnf(c_4821,plain,
( ~ in(X0,union(X1))
| ~ epsilon_transitive(X1)
| subset(sK5(X1,X0),X1) ),
inference(superposition,[status(thm)],[c_75,c_61]) ).
cnf(c_4822,plain,
( ~ in(X0,union(X1))
| ~ ordinal(X1)
| ordinal(sK5(X1,X0)) ),
inference(superposition,[status(thm)],[c_75,c_121]) ).
cnf(c_4898,plain,
( ~ in(X0,union(X1))
| ~ ordinal(sK5(X1,X0))
| ordinal(X0) ),
inference(superposition,[status(thm)],[c_76,c_121]) ).
cnf(c_7276,plain,
( ~ element(sK0(union(sK19)),sK19)
| in(sK0(union(sK19)),sK19)
| empty(sK19) ),
inference(instantiation,[status(thm)],[c_4260]) ).
cnf(c_8413,plain,
( ~ in(sK1(union(sK19)),union(sK19))
| ~ ordinal(sK5(sK19,sK1(union(sK19))))
| ordinal(sK1(union(sK19))) ),
inference(instantiation,[status(thm)],[c_4898]) ).
cnf(c_8415,plain,
( ~ in(sK1(union(sK19)),union(sK19))
| ~ ordinal(sK19)
| ordinal(sK5(sK19,sK1(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_4822]) ).
cnf(c_8432,plain,
( ~ in(sK2(union(sK19)),union(sK19))
| ~ ordinal(sK5(sK19,sK2(union(sK19))))
| ordinal(sK2(union(sK19))) ),
inference(instantiation,[status(thm)],[c_4898]) ).
cnf(c_8434,plain,
( ~ in(sK2(union(sK19)),union(sK19))
| ~ ordinal(sK19)
| ordinal(sK5(sK19,sK2(union(sK19)))) ),
inference(instantiation,[status(thm)],[c_4822]) ).
cnf(c_8479,plain,
( sK2(union(sK19)) != X0
| sK1(union(sK19)) != X0
| sK2(union(sK19)) = sK1(union(sK19)) ),
inference(instantiation,[status(thm)],[c_2611]) ).
cnf(c_9244,plain,
( ~ ordinal(sK1(union(sK19)))
| ~ ordinal(X0)
| sK1(union(sK19)) = X0
| in(sK1(union(sK19)),X0)
| in(X0,sK1(union(sK19))) ),
inference(instantiation,[status(thm)],[c_122]) ).
cnf(c_10463,plain,
( ~ in(X0,sK5(sK19,X0))
| ~ subset(sK5(sK19,X0),X1)
| element(X0,X1) ),
inference(instantiation,[status(thm)],[c_331]) ).
cnf(c_11749,plain,
( ~ in(X0,sK19)
| subset(X0,union(sK19)) ),
inference(instantiation,[status(thm)],[c_133]) ).
cnf(c_13443,plain,
( ~ in(X0,sK5(sK19,X0))
| ~ subset(sK5(sK19,X0),sK19)
| element(X0,sK19) ),
inference(instantiation,[status(thm)],[c_10463]) ).
cnf(c_21257,plain,
( ~ in(sK2(union(sK19)),sK1(union(sK19)))
| epsilon_connected(union(sK19)) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_21633,plain,
( ~ ordinal(sK2(union(sK19)))
| ~ ordinal(sK1(union(sK19)))
| sK1(union(sK19)) = sK2(union(sK19))
| in(sK2(union(sK19)),sK1(union(sK19)))
| in(sK1(union(sK19)),sK2(union(sK19))) ),
inference(instantiation,[status(thm)],[c_9244]) ).
cnf(c_26019,plain,
( sK2(union(sK19)) != sK2(union(sK19))
| sK1(union(sK19)) != sK2(union(sK19))
| sK2(union(sK19)) = sK1(union(sK19)) ),
inference(instantiation,[status(thm)],[c_8479]) ).
cnf(c_26272,plain,
( ~ in(sK0(union(sK19)),sK5(sK19,sK0(union(sK19))))
| ~ subset(sK5(sK19,sK0(union(sK19))),sK19)
| element(sK0(union(sK19)),sK19) ),
inference(instantiation,[status(thm)],[c_13443]) ).
cnf(c_26617,plain,
( ~ in(sK0(union(sK19)),sK19)
| subset(sK0(union(sK19)),union(sK19)) ),
inference(instantiation,[status(thm)],[c_11749]) ).
cnf(c_27408,plain,
( ~ in(sK1(union(sK19)),sK2(union(sK19)))
| epsilon_connected(union(sK19)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_27656,plain,
sK2(union(sK19)) = sK2(union(sK19)),
inference(instantiation,[status(thm)],[c_2609]) ).
cnf(c_46207,plain,
( ~ in(sK0(union(sK19)),union(sK19))
| ~ epsilon_transitive(sK19)
| subset(sK5(sK19,sK0(union(sK19))),sK19) ),
inference(instantiation,[status(thm)],[c_4821]) ).
cnf(c_46216,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_46207,c_27656,c_27408,c_26617,c_26272,c_26019,c_21633,c_21257,c_8432,c_8434,c_8413,c_8415,c_7276,c_4481,c_3937,c_3800,c_3719,c_3662,c_3663,c_3664,c_3618,c_3607,c_3608,c_3586,c_3584,c_124,c_81,c_88,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 09:15:17 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 39.02/6.20 % SZS status Started for theBenchmark.p
% 39.02/6.20 % SZS status Theorem for theBenchmark.p
% 39.02/6.20
% 39.02/6.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 39.02/6.20
% 39.02/6.20 ------ iProver source info
% 39.02/6.20
% 39.02/6.20 git: date: 2023-05-31 18:12:56 +0000
% 39.02/6.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 39.02/6.20 git: non_committed_changes: false
% 39.02/6.20 git: last_make_outside_of_git: false
% 39.02/6.20
% 39.02/6.20 ------ Parsing...
% 39.02/6.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 39.02/6.20
% 39.02/6.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 39.02/6.20
% 39.02/6.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 39.02/6.20
% 39.02/6.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 39.02/6.20 ------ Proving...
% 39.02/6.20 ------ Problem Properties
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20 clauses 58
% 39.02/6.20 conjectures 2
% 39.02/6.20 EPR 40
% 39.02/6.20 Horn 49
% 39.02/6.20 unary 20
% 39.02/6.20 binary 22
% 39.02/6.20 lits 121
% 39.02/6.20 lits eq 8
% 39.02/6.20 fd_pure 0
% 39.02/6.20 fd_pseudo 0
% 39.02/6.20 fd_cond 1
% 39.02/6.20 fd_pseudo_cond 6
% 39.02/6.20 AC symbols 0
% 39.02/6.20
% 39.02/6.20 ------ Input Options Time Limit: Unbounded
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20 ------
% 39.02/6.20 Current options:
% 39.02/6.20 ------
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20 ------ Proving...
% 39.02/6.20
% 39.02/6.20
% 39.02/6.20 % SZS status Theorem for theBenchmark.p
% 39.02/6.20
% 39.02/6.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 39.02/6.21
% 39.02/6.21
%------------------------------------------------------------------------------