TSTP Solution File: SEU232+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU232+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 17:05:00 EDT 2023
% Result : Theorem 27.85s 4.71s
% Output : CNFRefutation 27.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 195 ( 26 unt; 0 def)
% Number of atoms : 627 ( 69 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 741 ( 309 ~; 316 |; 90 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 281 ( 1 sgn; 159 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f6,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f7,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f8,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(f9,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f16,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f20,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f36,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f37,axiom,
! [X0,X1,X2] :
~ ( in(X2,X0)
& in(X1,X2)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f38,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(f52,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f58,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f61,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
? [X0,X1] :
( ~ ordinal(X0)
& in(X0,X1)
& ordinal(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
? [X0,X1] :
( ~ ordinal(X0)
& in(X0,X1)
& ordinal(X1) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f69,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f72,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f75,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f78,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,[],[f60]) ).
fof(f79,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f81,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])],[f79,f80]) ).
fof(f82,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,[],[f61]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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(f85,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])],[f83,f84]) ).
fof(f86,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,[],[f62]) ).
fof(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f89,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])],[f87,f88]) ).
fof(f90,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f91,plain,
! [X0] :
( ( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) )
& ( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f94,f95]) ).
fof(f97,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f16,f97]) ).
fof(f119,plain,
( ? [X0,X1] :
( ~ ordinal(X0)
& in(X0,X1)
& ordinal(X1) )
=> ( ~ ordinal(sK16)
& in(sK16,sK17)
& ordinal(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
( ~ ordinal(sK16)
& in(sK16,sK17)
& ordinal(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f67,f119]) ).
fof(f121,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f124,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f131,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f132,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f133,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
! [X3,X0,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f137,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f139,plain,
! [X0] :
( epsilon_connected(X0)
| sK1(X0) != sK2(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f140,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f141,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f142,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f144,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f145,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f149,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f96]) ).
fof(f153,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f98]) ).
fof(f158,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f181,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f120]) ).
fof(f182,plain,
in(sK16,sK17),
inference(cnf_transformation,[],[f120]) ).
fof(f183,plain,
~ ordinal(sK16),
inference(cnf_transformation,[],[f120]) ).
fof(f184,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f185,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f36]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f188,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f190,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f193,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f197,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f149]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_54,plain,
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_55,plain,
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_56,plain,
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_57,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_58,plain,
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_59,plain,
( sK2(X0) != sK1(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_60,plain,
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_61,plain,
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_62,plain,
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_63,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| ~ epsilon_connected(X1)
| X0 = X2
| in(X0,X2)
| in(X2,X0) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_64,plain,
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_65,plain,
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_66,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_68,plain,
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_69,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_73,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_76,plain,
element(sK5(X0),X0),
inference(cnf_transformation,[],[f153]) ).
cnf(c_82,plain,
empty(empty_set),
inference(cnf_transformation,[],[f158]) ).
cnf(c_104,negated_conjecture,
~ ordinal(sK16),
inference(cnf_transformation,[],[f183]) ).
cnf(c_105,negated_conjecture,
in(sK16,sK17),
inference(cnf_transformation,[],[f182]) ).
cnf(c_106,negated_conjecture,
ordinal(sK17),
inference(cnf_transformation,[],[f181]) ).
cnf(c_107,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_108,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f185]) ).
cnf(c_109,plain,
( ~ in(X0,X1)
| ~ in(X1,X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_110,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_113,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f190]) ).
cnf(c_116,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_144,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_110]) ).
cnf(c_166,plain,
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(prop_impl_just,[status(thm)],[c_68]) ).
cnf(c_168,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
cnf(c_172,plain,
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
cnf(c_173,plain,
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(renaming,[status(thm)],[c_172]) ).
cnf(c_174,plain,
( epsilon_connected(X0)
| sK2(X0) != sK1(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
cnf(c_175,plain,
( sK2(X0) != sK1(X0)
| epsilon_connected(X0) ),
inference(renaming,[status(thm)],[c_174]) ).
cnf(c_176,plain,
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
cnf(c_177,plain,
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(renaming,[status(thm)],[c_176]) ).
cnf(c_178,plain,
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
cnf(c_179,plain,
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(renaming,[status(thm)],[c_178]) ).
cnf(c_180,plain,
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
cnf(c_181,plain,
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(renaming,[status(thm)],[c_180]) ).
cnf(c_312,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_113,c_144]) ).
cnf(c_761,plain,
( X0 != sK16
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_104]) ).
cnf(c_762,plain,
( ~ epsilon_connected(sK16)
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_761]) ).
cnf(c_769,plain,
( X0 != sK17
| epsilon_transitive(X0) ),
inference(resolution_lifted,[status(thm)],[c_168,c_106]) ).
cnf(c_770,plain,
epsilon_transitive(sK17),
inference(unflattening,[status(thm)],[c_769]) ).
cnf(c_774,plain,
( X0 != sK17
| epsilon_connected(X0) ),
inference(resolution_lifted,[status(thm)],[c_166,c_106]) ).
cnf(c_775,plain,
epsilon_connected(sK17),
inference(unflattening,[status(thm)],[c_774]) ).
cnf(c_1075,plain,
( X0 != sK16
| ~ epsilon_transitive(sK16)
| in(sK1(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_181,c_762]) ).
cnf(c_1076,plain,
( ~ epsilon_transitive(sK16)
| in(sK1(sK16),sK16) ),
inference(unflattening,[status(thm)],[c_1075]) ).
cnf(c_1083,plain,
( X0 != sK16
| ~ epsilon_transitive(sK16)
| in(sK2(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_179,c_762]) ).
cnf(c_1084,plain,
( ~ epsilon_transitive(sK16)
| in(sK2(sK16),sK16) ),
inference(unflattening,[status(thm)],[c_1083]) ).
cnf(c_1091,plain,
( X0 != sK16
| ~ in(sK1(X0),sK2(X0))
| ~ epsilon_transitive(sK16) ),
inference(resolution_lifted,[status(thm)],[c_177,c_762]) ).
cnf(c_1092,plain,
( ~ in(sK1(sK16),sK2(sK16))
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_1091]) ).
cnf(c_1099,plain,
( sK2(X0) != sK1(X0)
| X0 != sK16
| ~ epsilon_transitive(sK16) ),
inference(resolution_lifted,[status(thm)],[c_175,c_762]) ).
cnf(c_1100,plain,
( sK2(sK16) != sK1(sK16)
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_1099]) ).
cnf(c_1107,plain,
( X0 != sK16
| ~ in(sK2(X0),sK1(X0))
| ~ epsilon_transitive(sK16) ),
inference(resolution_lifted,[status(thm)],[c_173,c_762]) ).
cnf(c_1108,plain,
( ~ in(sK2(sK16),sK1(sK16))
| ~ epsilon_transitive(sK16) ),
inference(unflattening,[status(thm)],[c_1107]) ).
cnf(c_2537,plain,
X0 = X0,
theory(equality) ).
cnf(c_2540,plain,
( X0 != X1
| X2 != X3
| ~ in(X1,X3)
| in(X0,X2) ),
theory(equality) ).
cnf(c_3429,plain,
~ empty(sK17),
inference(superposition,[status(thm)],[c_105,c_116]) ).
cnf(c_3967,plain,
( ~ epsilon_transitive(sK17)
| subset(sK16,sK17) ),
inference(superposition,[status(thm)],[c_105,c_57]) ).
cnf(c_3976,plain,
subset(sK16,sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_3967,c_770]) ).
cnf(c_4613,plain,
( ~ in(X0,X1)
| ~ in(sK16,X1)
| ~ epsilon_connected(X1)
| X0 = sK16
| in(X0,sK16)
| in(sK16,X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_4903,plain,
~ empty(sK17),
inference(superposition,[status(thm)],[c_105,c_116]) ).
cnf(c_4909,plain,
( ~ subset(sK0(sK16),sK16)
| epsilon_transitive(sK16) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_4910,plain,
( in(sK0(sK16),sK16)
| epsilon_transitive(sK16) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_5827,plain,
( ~ in(sK0(sK16),sK16)
| ~ subset(sK16,X0)
| in(sK0(sK16),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_5976,plain,
( in(sK3(sK0(sK16),sK16),sK0(sK16))
| subset(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_5977,plain,
( ~ in(sK3(sK0(sK16),sK16),sK16)
| subset(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_6433,plain,
sK17 = sK17,
inference(instantiation,[status(thm)],[c_2537]) ).
cnf(c_6698,plain,
( ~ in(X0,sK17)
| ~ in(sK16,sK17)
| ~ epsilon_connected(sK17)
| X0 = sK16
| in(X0,sK16)
| in(sK16,X0) ),
inference(instantiation,[status(thm)],[c_4613]) ).
cnf(c_7143,plain,
( ~ in(sK2(sK16),sK16)
| ~ subset(sK16,X0)
| in(sK2(sK16),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_7193,plain,
( ~ in(sK1(sK16),sK16)
| ~ subset(sK16,X0)
| in(sK1(sK16),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
cnf(c_7376,plain,
( ~ in(sK2(sK16),X0)
| ~ in(sK1(sK16),X0)
| ~ epsilon_connected(X0)
| sK2(sK16) = sK1(sK16)
| in(sK2(sK16),sK1(sK16))
| in(sK1(sK16),sK2(sK16)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_14025,plain,
( ~ in(sK3(sK0(sK16),sK16),sK0(sK16))
| in(sK3(sK0(sK16),sK16),set_difference(sK0(sK16),X0))
| in(sK3(sK0(sK16),sK16),X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_14033,plain,
( ~ in(sK3(sK0(sK16),sK16),sK0(sK16))
| ~ in(sK0(sK16),sK3(sK0(sK16),sK16)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_14040,plain,
( ~ in(sK3(sK0(sK16),sK16),sK0(sK16))
| in(sK3(sK0(sK16),sK16),set_difference(sK0(sK16),empty_set))
| in(sK3(sK0(sK16),sK16),empty_set) ),
inference(instantiation,[status(thm)],[c_14025]) ).
cnf(c_15224,plain,
( ~ in(sK0(sK16),sK16)
| ~ subset(sK16,sK17)
| in(sK0(sK16),sK17) ),
inference(instantiation,[status(thm)],[c_5827]) ).
cnf(c_28692,plain,
( in(sK5(X0),X0)
| empty(X0) ),
inference(superposition,[status(thm)],[c_76,c_107]) ).
cnf(c_29596,plain,
( ~ in(X0,sK17)
| ~ epsilon_connected(sK17)
| X0 = sK16
| in(X0,sK16)
| in(sK16,X0) ),
inference(superposition,[status(thm)],[c_105,c_63]) ).
cnf(c_29609,plain,
( ~ in(X0,sK17)
| X0 = sK16
| in(X0,sK16)
| in(sK16,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29596,c_775]) ).
cnf(c_29866,plain,
( sK5(sK17) = sK16
| in(sK5(sK17),sK16)
| in(sK16,sK5(sK17))
| empty(sK17) ),
inference(superposition,[status(thm)],[c_28692,c_29609]) ).
cnf(c_29875,plain,
( sK5(sK17) = sK16
| in(sK5(sK17),sK16)
| in(sK16,sK5(sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29866,c_4903]) ).
cnf(c_30072,plain,
( ~ epsilon_transitive(sK16)
| sK5(sK17) = sK16
| in(sK16,sK5(sK17))
| subset(sK5(sK17),sK16) ),
inference(superposition,[status(thm)],[c_29875,c_57]) ).
cnf(c_33288,plain,
( ~ in(sK1(sK16),sK16)
| ~ subset(sK16,sK17)
| in(sK1(sK16),sK17) ),
inference(instantiation,[status(thm)],[c_7193]) ).
cnf(c_48360,plain,
( ~ in(sK2(sK16),sK17)
| ~ in(sK1(sK16),sK17)
| ~ epsilon_connected(sK17)
| sK2(sK16) = sK1(sK16)
| in(sK2(sK16),sK1(sK16))
| in(sK1(sK16),sK2(sK16)) ),
inference(instantiation,[status(thm)],[c_7376]) ).
cnf(c_56046,plain,
( ~ in(sK2(sK16),sK16)
| ~ subset(sK16,sK17)
| in(sK2(sK16),sK17) ),
inference(instantiation,[status(thm)],[c_7143]) ).
cnf(c_71010,plain,
set_difference(sK0(sK16),empty_set) = sK0(sK16),
inference(instantiation,[status(thm)],[c_108]) ).
cnf(c_71013,plain,
sK0(sK16) = sK0(sK16),
inference(instantiation,[status(thm)],[c_2537]) ).
cnf(c_99943,plain,
~ epsilon_transitive(sK16),
inference(global_subsumption_just,[status(thm)],[c_30072,c_775,c_1076,c_1084,c_1092,c_1100,c_1108,c_3976,c_33288,c_48360,c_56046]) ).
cnf(c_104875,plain,
( ~ in(sK3(sK0(sK16),sK16),sK17)
| ~ in(sK16,sK17)
| ~ epsilon_connected(sK17)
| sK3(sK0(sK16),sK16) = sK16
| in(sK3(sK0(sK16),sK16),sK16)
| in(sK16,sK3(sK0(sK16),sK16)) ),
inference(instantiation,[status(thm)],[c_6698]) ).
cnf(c_119844,plain,
( ~ element(X0,sK17)
| in(X0,sK17)
| empty(sK17) ),
inference(instantiation,[status(thm)],[c_107]) ).
cnf(c_119919,plain,
( X0 != X1
| X2 != sK17
| ~ in(X1,sK17)
| in(X0,X2) ),
inference(instantiation,[status(thm)],[c_2540]) ).
cnf(c_119953,plain,
( X0 != sK0(sK16)
| X1 != sK16
| ~ in(sK0(sK16),sK16)
| in(X0,X1) ),
inference(instantiation,[status(thm)],[c_2540]) ).
cnf(c_120414,plain,
( ~ in(sK3(sK0(sK16),sK16),sK0(sK16))
| ~ in(X0,sK3(sK0(sK16),sK16))
| ~ in(sK0(sK16),X0) ),
inference(instantiation,[status(thm)],[c_109]) ).
cnf(c_120630,plain,
( X0 != X1
| sK17 != sK17
| ~ in(X1,sK17)
| in(X0,sK17) ),
inference(instantiation,[status(thm)],[c_119919]) ).
cnf(c_123070,plain,
( ~ in(sK3(sK0(sK16),sK16),X0)
| ~ empty(X0) ),
inference(instantiation,[status(thm)],[c_116]) ).
cnf(c_123071,plain,
( ~ in(sK3(sK0(sK16),sK16),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_123070]) ).
cnf(c_123118,plain,
( ~ in(sK3(sK0(sK16),sK16),sK0(sK16))
| ~ in(sK16,sK3(sK0(sK16),sK16))
| ~ in(sK0(sK16),sK16) ),
inference(instantiation,[status(thm)],[c_120414]) ).
cnf(c_123838,plain,
( ~ element(sK3(sK0(sK16),sK16),sK17)
| in(sK3(sK0(sK16),sK16),sK17)
| empty(sK17) ),
inference(instantiation,[status(thm)],[c_119844]) ).
cnf(c_124900,plain,
( ~ in(X0,X1)
| ~ subset(X1,sK17)
| element(X0,sK17) ),
inference(instantiation,[status(thm)],[c_312]) ).
cnf(c_127322,plain,
( X0 != sK0(sK16)
| sK17 != sK17
| ~ in(sK0(sK16),sK17)
| in(X0,sK17) ),
inference(instantiation,[status(thm)],[c_120630]) ).
cnf(c_129911,plain,
( ~ in(sK3(sK0(sK16),sK16),set_difference(sK0(sK16),X0))
| ~ subset(set_difference(sK0(sK16),X0),sK17)
| element(sK3(sK0(sK16),sK16),sK17) ),
inference(instantiation,[status(thm)],[c_124900]) ).
cnf(c_129912,plain,
( ~ in(sK3(sK0(sK16),sK16),set_difference(sK0(sK16),empty_set))
| ~ subset(set_difference(sK0(sK16),empty_set),sK17)
| element(sK3(sK0(sK16),sK16),sK17) ),
inference(instantiation,[status(thm)],[c_129911]) ).
cnf(c_133826,plain,
( set_difference(sK0(sK16),empty_set) != sK0(sK16)
| sK17 != sK17
| ~ in(sK0(sK16),sK17)
| in(set_difference(sK0(sK16),empty_set),sK17) ),
inference(instantiation,[status(thm)],[c_127322]) ).
cnf(c_141058,plain,
( ~ in(set_difference(sK0(sK16),X0),sK17)
| ~ epsilon_transitive(sK17)
| subset(set_difference(sK0(sK16),X0),sK17) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_141059,plain,
( ~ in(set_difference(sK0(sK16),empty_set),sK17)
| ~ epsilon_transitive(sK17)
| subset(set_difference(sK0(sK16),empty_set),sK17) ),
inference(instantiation,[status(thm)],[c_141058]) ).
cnf(c_144597,plain,
( sK3(sK0(sK16),sK16) != sK16
| X0 != sK0(sK16)
| ~ in(sK0(sK16),sK16)
| in(X0,sK3(sK0(sK16),sK16)) ),
inference(instantiation,[status(thm)],[c_119953]) ).
cnf(c_153738,plain,
( sK3(sK0(sK16),sK16) != sK16
| sK0(sK16) != sK0(sK16)
| ~ in(sK0(sK16),sK16)
| in(sK0(sK16),sK3(sK0(sK16),sK16)) ),
inference(instantiation,[status(thm)],[c_144597]) ).
cnf(c_153739,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_153738,c_141059,c_133826,c_129912,c_123838,c_123118,c_123071,c_104875,c_99943,c_71013,c_71010,c_15224,c_14040,c_14033,c_6433,c_5976,c_5977,c_4909,c_4910,c_3976,c_3429,c_775,c_770,c_105,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU232+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n025.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 18:42:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.85/4.71 % SZS status Started for theBenchmark.p
% 27.85/4.71 % SZS status Theorem for theBenchmark.p
% 27.85/4.71
% 27.85/4.71 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.85/4.71
% 27.85/4.71 ------ iProver source info
% 27.85/4.71
% 27.85/4.71 git: date: 2023-05-31 18:12:56 +0000
% 27.85/4.71 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.85/4.71 git: non_committed_changes: false
% 27.85/4.71 git: last_make_outside_of_git: false
% 27.85/4.71
% 27.85/4.71 ------ Parsing...
% 27.85/4.71 ------ Clausification by vclausify_rel & Parsing by iProver...
% 27.85/4.71
% 27.85/4.71 ------ Preprocessing... sup_sim: 0 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 27.85/4.71
% 27.85/4.71 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 27.85/4.71
% 27.85/4.71 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.85/4.71 ------ Proving...
% 27.85/4.71 ------ Problem Properties
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71 clauses 49
% 27.85/4.71 conjectures 1
% 27.85/4.71 EPR 27
% 27.85/4.71 Horn 39
% 27.85/4.71 unary 17
% 27.85/4.71 binary 19
% 27.85/4.71 lits 98
% 27.85/4.71 lits eq 11
% 27.85/4.71 fd_pure 0
% 27.85/4.71 fd_pseudo 0
% 27.85/4.71 fd_cond 1
% 27.85/4.71 fd_pseudo_cond 5
% 27.85/4.71 AC symbols 0
% 27.85/4.71
% 27.85/4.71 ------ Schedule dynamic 5 is on
% 27.85/4.71
% 27.85/4.71 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71 ------
% 27.85/4.71 Current options:
% 27.85/4.71 ------
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71 ------ Proving...
% 27.85/4.71
% 27.85/4.71
% 27.85/4.71 % SZS status Theorem for theBenchmark.p
% 27.85/4.71
% 27.85/4.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.85/4.71
% 27.85/4.71
%------------------------------------------------------------------------------