TSTP Solution File: NUM402+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM402+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : Fri May 3 02:49:10 EDT 2024
% Result : Theorem 71.41s 10.73s
% Output : CNFRefutation 71.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 112 ( 4 unt; 0 def)
% Number of atoms : 411 ( 29 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 487 ( 188 ~; 195 |; 78 &)
% ( 9 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 195 ( 0 sgn 133 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f11,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f34,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f37,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ordinal(X1) )
=> ordinal(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_ordinal1) ).
fof(f38,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ordinal(X1) )
=> ordinal(union(X0)) ),
inference(negated_conjecture,[],[f37]) ).
fof(f64,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f69,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1) )
| ~ ordinal(X0) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
? [X0] :
( ~ ordinal(union(X0))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,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,[],[f64]) ).
fof(f83,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,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])],[f83,f84]) ).
fof(f86,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,[],[f65]) ).
fof(f87,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,[],[f86]) ).
fof(f88,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(f89,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])],[f87,f88]) ).
fof(f90,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f91,f92]) ).
fof(f94,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f95,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f94]) ).
fof(f96,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(f97,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,[],[f96]) ).
fof(f98,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(sK4(X0,X1),X3) )
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK4(X0,X1),X4) )
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK4(X0,X1),X4) )
=> ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK4(X0,X1),X3) )
| ~ in(sK4(X0,X1),X1) )
& ( ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f97,f100,f99,f98]) ).
fof(f130,plain,
( ? [X0] :
( ~ ordinal(union(X0))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,X0) ) )
=> ( ~ ordinal(union(sK21))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,sK21) ) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ~ ordinal(union(sK21))
& ! [X1] :
( ordinal(X1)
| ~ in(X1,sK21) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f75,f130]) ).
fof(f144,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f145,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f146,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f148,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f149,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f151,plain,
! [X0] :
( epsilon_connected(X0)
| sK1(X0) != sK2(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f153,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f154,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f156,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
! [X0,X1,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
! [X0,X1,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f213,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f214,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f216,plain,
! [X1] :
( ordinal(X1)
| ~ in(X1,sK21) ),
inference(cnf_transformation,[],[f131]) ).
fof(f217,plain,
~ ordinal(union(sK21)),
inference(cnf_transformation,[],[f131]) ).
fof(f225,plain,
! [X0,X6,X5] :
( in(X5,union(X0))
| ~ in(X6,X0)
| ~ in(X5,X6) ),
inference(equality_resolution,[],[f161]) ).
fof(f226,plain,
! [X0,X5] :
( in(sK6(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f160]) ).
fof(f227,plain,
! [X0,X5] :
( in(X5,sK6(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f159]) ).
cnf(c_58,plain,
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_59,plain,
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_61,plain,
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_62,plain,
( sK2(X0) != sK1(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_63,plain,
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_64,plain,
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_65,plain,
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_67,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_68,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_69,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_70,plain,
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_72,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_76,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| in(X0,union(X2)) ),
inference(cnf_transformation,[],[f225]) ).
cnf(c_77,plain,
( ~ in(X0,union(X1))
| in(sK6(X1,X0),X1) ),
inference(cnf_transformation,[],[f226]) ).
cnf(c_78,plain,
( ~ in(X0,union(X1))
| in(X0,sK6(X1,X0)) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_127,plain,
( ~ in(X0,X1)
| ~ ordinal(X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_128,plain,
( ~ ordinal(X0)
| ~ ordinal(X1)
| X0 = X1
| in(X0,X1)
| in(X1,X0) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_130,negated_conjecture,
~ ordinal(union(sK21)),
inference(cnf_transformation,[],[f217]) ).
cnf(c_131,negated_conjecture,
( ~ in(X0,sK21)
| ordinal(X0) ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_3320,plain,
( ~ epsilon_connected(union(sK21))
| ~ epsilon_transitive(union(sK21))
| ordinal(union(sK21)) ),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_3348,plain,
( ~ subset(sK0(union(sK21)),union(sK21))
| epsilon_transitive(union(sK21)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_3349,plain,
( in(sK0(union(sK21)),union(sK21))
| epsilon_transitive(union(sK21)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_3445,plain,
( sK2(union(sK21)) != sK1(union(sK21))
| epsilon_connected(union(sK21)) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_3446,plain,
( in(sK1(union(sK21)),union(sK21))
| epsilon_connected(union(sK21)) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_3447,plain,
( in(sK2(union(sK21)),union(sK21))
| epsilon_connected(union(sK21)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_3448,plain,
( ~ in(sK1(union(sK21)),sK2(union(sK21)))
| epsilon_connected(union(sK21)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_3449,plain,
( ~ in(sK2(union(sK21)),sK1(union(sK21)))
| epsilon_connected(union(sK21)) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_3466,plain,
( ~ in(sK0(union(sK21)),union(sK21))
| in(sK6(sK21,sK0(union(sK21))),sK21) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_3896,plain,
( in(sK3(sK0(union(sK21)),union(sK21)),sK0(union(sK21)))
| subset(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_3897,plain,
( ~ in(sK3(sK0(union(sK21)),union(sK21)),union(sK21))
| subset(sK0(union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_3968,plain,
( ~ in(sK1(union(sK21)),union(sK21))
| in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_3973,plain,
( ~ ordinal(sK2(union(sK21)))
| ~ ordinal(sK1(union(sK21)))
| sK2(union(sK21)) = sK1(union(sK21))
| in(sK2(union(sK21)),sK1(union(sK21)))
| in(sK1(union(sK21)),sK2(union(sK21))) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_3990,plain,
( ~ in(sK2(union(sK21)),union(sK21))
| in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_78]) ).
cnf(c_4457,plain,
( ~ in(X0,union(sK21))
| ordinal(sK6(sK21,X0)) ),
inference(superposition,[status(thm)],[c_77,c_131]) ).
cnf(c_4469,plain,
( ~ in(X0,union(X1))
| ~ epsilon_transitive(sK6(X1,X0))
| subset(X0,sK6(X1,X0)) ),
inference(superposition,[status(thm)],[c_78,c_60]) ).
cnf(c_5375,plain,
( ordinal(sK6(sK21,sK0(union(sK21))))
| epsilon_transitive(union(sK21)) ),
inference(superposition,[status(thm)],[c_59,c_4457]) ).
cnf(c_5377,plain,
( ordinal(sK6(sK21,sK2(union(sK21))))
| epsilon_connected(union(sK21)) ),
inference(superposition,[status(thm)],[c_64,c_4457]) ).
cnf(c_5384,plain,
( ordinal(sK6(sK21,sK1(union(sK21))))
| epsilon_connected(union(sK21)) ),
inference(superposition,[status(thm)],[c_65,c_4457]) ).
cnf(c_5412,plain,
( ~ in(sK1(union(sK21)),sK6(sK21,sK1(union(sK21))))
| ~ ordinal(sK6(sK21,sK1(union(sK21))))
| ordinal(sK1(union(sK21))) ),
inference(instantiation,[status(thm)],[c_127]) ).
cnf(c_5423,plain,
( epsilon_transitive(sK6(sK21,sK0(union(sK21))))
| epsilon_transitive(union(sK21)) ),
inference(superposition,[status(thm)],[c_5375,c_72]) ).
cnf(c_5447,plain,
( epsilon_transitive(sK6(sK21,sK2(union(sK21))))
| epsilon_connected(union(sK21)) ),
inference(superposition,[status(thm)],[c_5377,c_72]) ).
cnf(c_5492,plain,
( ~ in(sK2(union(sK21)),sK6(sK21,sK2(union(sK21))))
| ~ ordinal(sK6(sK21,sK2(union(sK21))))
| ordinal(sK2(union(sK21))) ),
inference(instantiation,[status(thm)],[c_127]) ).
cnf(c_5580,plain,
epsilon_connected(union(sK21)),
inference(global_subsumption_just,[status(thm)],[c_5447,c_3449,c_3448,c_3447,c_3446,c_3445,c_3968,c_3973,c_3990,c_5377,c_5384,c_5412,c_5492]) ).
cnf(c_39592,plain,
( ~ in(sK0(union(sK21)),union(sK21))
| ~ epsilon_transitive(sK6(sK21,sK0(union(sK21))))
| subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_4469]) ).
cnf(c_39845,plain,
( ~ in(X0,X1)
| ~ in(X1,sK21)
| in(X0,union(sK21)) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_41076,plain,
( ~ in(sK3(sK0(union(sK21)),union(sK21)),sK0(union(sK21)))
| ~ subset(sK0(union(sK21)),X0)
| in(sK3(sK0(union(sK21)),union(sK21)),X0) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_47873,plain,
( ~ in(sK3(sK0(union(sK21)),union(sK21)),sK0(union(sK21)))
| ~ subset(sK0(union(sK21)),sK6(sK21,sK0(union(sK21))))
| in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21)))) ),
inference(instantiation,[status(thm)],[c_41076]) ).
cnf(c_51977,plain,
( ~ in(sK3(sK0(union(sK21)),union(sK21)),sK6(sK21,sK0(union(sK21))))
| ~ in(sK6(sK21,sK0(union(sK21))),sK21)
| in(sK3(sK0(union(sK21)),union(sK21)),union(sK21)) ),
inference(instantiation,[status(thm)],[c_39845]) ).
cnf(c_51988,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_51977,c_47873,c_39592,c_5580,c_5423,c_3896,c_3897,c_3466,c_3348,c_3349,c_3320,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM402+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 19:54:03 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 71.41/10.73 % SZS status Started for theBenchmark.p
% 71.41/10.73 % SZS status Theorem for theBenchmark.p
% 71.41/10.73
% 71.41/10.73 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 71.41/10.73
% 71.41/10.73 ------ iProver source info
% 71.41/10.73
% 71.41/10.73 git: date: 2024-05-02 19:28:25 +0000
% 71.41/10.73 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 71.41/10.73 git: non_committed_changes: false
% 71.41/10.73
% 71.41/10.73 ------ Parsing...
% 71.41/10.73 ------ Clausification by vclausify_rel & Parsing by iProver...
% 71.41/10.73
% 71.41/10.73 ------ 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
% 71.41/10.73
% 71.41/10.73 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 71.41/10.73
% 71.41/10.73 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 71.41/10.73 ------ Proving...
% 71.41/10.73 ------ Problem Properties
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73 clauses 61
% 71.41/10.73 conjectures 2
% 71.41/10.73 EPR 39
% 71.41/10.73 Horn 52
% 71.41/10.73 unary 23
% 71.41/10.73 binary 24
% 71.41/10.73 lits 119
% 71.41/10.73 lits eq 8
% 71.41/10.73 fd_pure 0
% 71.41/10.73 fd_pseudo 0
% 71.41/10.73 fd_cond 1
% 71.41/10.73 fd_pseudo_cond 6
% 71.41/10.73 AC symbols 0
% 71.41/10.73
% 71.41/10.73 ------ Input Options Time Limit: Unbounded
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73 ------
% 71.41/10.73 Current options:
% 71.41/10.73 ------
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73 ------ Proving...
% 71.41/10.73
% 71.41/10.73
% 71.41/10.73 % SZS status Theorem for theBenchmark.p
% 71.41/10.73
% 71.41/10.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.41/10.73
% 71.41/10.73
%------------------------------------------------------------------------------