TSTP Solution File: SEU339+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU339+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 17:06:15 EDT 2023
% Result : Theorem 3.40s 1.17s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 130 ( 27 unt; 0 def)
% Number of atoms : 445 ( 48 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 532 ( 217 ~; 197 |; 86 &)
% ( 9 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 269 ( 12 sgn; 155 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( antisymmetric_relstr(X0)
<=> is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f39,conjecture,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X2,X1)
& related(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( related(X0,X2,X1)
& related(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
inference(negated_conjecture,[],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f44,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f46,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f53,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( antisymmetric_relstr(X0)
<=> is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f59,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X2,X1)
& related(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& antisymmetric_relstr(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f65,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X2,X1)
& related(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& antisymmetric_relstr(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f67,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f73,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> ( sK0(X0,X1) != sK1(X0,X1)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ( sK0(X0,X1) != sK1(X0,X1)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(sK1(X0,X1),X1)
& in(sK0(X0,X1),X1) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f76,f77]) ).
fof(f79,plain,
! [X0] :
( ( ( antisymmetric_relstr(X0)
| ~ is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) )
& ( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ antisymmetric_relstr(X0) ) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(X0,X2,X1)
& related(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& rel_str(X0)
& antisymmetric_relstr(X0) )
=> ( ? [X1] :
( ? [X2] :
( X1 != X2
& related(sK10,X2,X1)
& related(sK10,X1,X2)
& element(X2,the_carrier(sK10)) )
& element(X1,the_carrier(sK10)) )
& rel_str(sK10)
& antisymmetric_relstr(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X1] :
( ? [X2] :
( X1 != X2
& related(sK10,X2,X1)
& related(sK10,X1,X2)
& element(X2,the_carrier(sK10)) )
& element(X1,the_carrier(sK10)) )
=> ( ? [X2] :
( sK11 != X2
& related(sK10,X2,sK11)
& related(sK10,sK11,X2)
& element(X2,the_carrier(sK10)) )
& element(sK11,the_carrier(sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ? [X2] :
( sK11 != X2
& related(sK10,X2,sK11)
& related(sK10,sK11,X2)
& element(X2,the_carrier(sK10)) )
=> ( sK11 != sK12
& related(sK10,sK12,sK11)
& related(sK10,sK11,sK12)
& element(sK12,the_carrier(sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( sK11 != sK12
& related(sK10,sK12,sK11)
& related(sK10,sK11,sK12)
& element(sK12,the_carrier(sK10))
& element(sK11,the_carrier(sK10))
& rel_str(sK10)
& antisymmetric_relstr(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f65,f102,f101,f100]) ).
fof(f105,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f53]) ).
fof(f106,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f107,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f114,plain,
! [X0] :
( is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f118,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f119,plain,
! [X0] :
( relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f135,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f142,plain,
antisymmetric_relstr(sK10),
inference(cnf_transformation,[],[f103]) ).
fof(f143,plain,
rel_str(sK10),
inference(cnf_transformation,[],[f103]) ).
fof(f144,plain,
element(sK11,the_carrier(sK10)),
inference(cnf_transformation,[],[f103]) ).
fof(f145,plain,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f103]) ).
fof(f146,plain,
related(sK10,sK11,sK12),
inference(cnf_transformation,[],[f103]) ).
fof(f147,plain,
related(sK10,sK12,sK11),
inference(cnf_transformation,[],[f103]) ).
fof(f148,plain,
sK11 != sK12,
inference(cnf_transformation,[],[f103]) ).
fof(f149,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f151,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f154,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f158,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f107,f113,f113]) ).
fof(f160,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f116,f113]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f138,f113]) ).
cnf(c_50,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f106]) ).
cnf(c_57,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),X2)
| ~ in(X0,X3)
| ~ in(X1,X3)
| ~ is_antisymmetric_in(X2,X3)
| ~ relation(X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_59,plain,
( ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_61,plain,
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0)) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_62,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_63,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_79,plain,
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_80,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_84,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_86,negated_conjecture,
sK11 != sK12,
inference(cnf_transformation,[],[f148]) ).
cnf(c_87,negated_conjecture,
related(sK10,sK12,sK11),
inference(cnf_transformation,[],[f147]) ).
cnf(c_88,negated_conjecture,
related(sK10,sK11,sK12),
inference(cnf_transformation,[],[f146]) ).
cnf(c_89,negated_conjecture,
element(sK12,the_carrier(sK10)),
inference(cnf_transformation,[],[f145]) ).
cnf(c_90,negated_conjecture,
element(sK11,the_carrier(sK10)),
inference(cnf_transformation,[],[f144]) ).
cnf(c_91,negated_conjecture,
rel_str(sK10),
inference(cnf_transformation,[],[f143]) ).
cnf(c_92,negated_conjecture,
antisymmetric_relstr(sK10),
inference(cnf_transformation,[],[f142]) ).
cnf(c_93,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_95,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_96,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_98,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_125,plain,
( ~ antisymmetric_relstr(sK10)
| ~ rel_str(sK10)
| is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_134,plain,
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_80]) ).
cnf(c_135,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_134]) ).
cnf(c_148,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_79,c_62]) ).
cnf(c_149,plain,
( ~ relation_of2(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_148]) ).
cnf(c_154,plain,
( ~ rel_str(X0)
| relation_of2_as_subset(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
cnf(c_166,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
cnf(c_579,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(demodulation,[status(thm)],[c_166,c_51]) ).
cnf(c_616,plain,
( ~ related(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0)) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
cnf(c_638,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ in(X0,X3)
| ~ in(X1,X3)
| ~ is_antisymmetric_in(X2,X3)
| ~ relation(X2)
| X0 = X1 ),
inference(demodulation,[status(thm)],[c_57,c_51]) ).
cnf(c_683,plain,
( the_InternalRel(X0) != X1
| the_carrier(X0) != X2
| the_carrier(X0) != X3
| ~ rel_str(X0)
| relation_of2(X1,X2,X3) ),
inference(resolution_lifted,[status(thm)],[c_135,c_154]) ).
cnf(c_684,plain,
( ~ rel_str(X0)
| relation_of2(the_InternalRel(X0),the_carrier(X0),the_carrier(X0)) ),
inference(unflattening,[status(thm)],[c_683]) ).
cnf(c_707,plain,
( the_InternalRel(X0) != X1
| the_carrier(X0) != X2
| the_carrier(X0) != X3
| ~ rel_str(X0)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(resolution_lifted,[status(thm)],[c_149,c_684]) ).
cnf(c_708,plain,
( ~ rel_str(X0)
| element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ),
inference(unflattening,[status(thm)],[c_707]) ).
cnf(c_728,plain,
( X0 != sK10
| ~ rel_str(X0)
| is_antisymmetric_in(the_InternalRel(X0),the_carrier(X0)) ),
inference(resolution_lifted,[status(thm)],[c_59,c_92]) ).
cnf(c_729,plain,
( ~ rel_str(sK10)
| is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10)) ),
inference(unflattening,[status(thm)],[c_728]) ).
cnf(c_730,plain,
is_antisymmetric_in(the_InternalRel(sK10),the_carrier(sK10)),
inference(global_subsumption_just,[status(thm)],[c_729,c_92,c_91,c_125]) ).
cnf(c_738,plain,
( X0 != sK10
| X1 != sK12
| X2 != sK11
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0)) ),
inference(resolution_lifted,[status(thm)],[c_616,c_87]) ).
cnf(c_739,plain,
( ~ element(sK11,the_carrier(sK10))
| ~ element(sK12,the_carrier(sK10))
| ~ rel_str(sK10)
| in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK11)),the_InternalRel(sK10)) ),
inference(unflattening,[status(thm)],[c_738]) ).
cnf(c_745,plain,
( X0 != sK10
| X1 != sK11
| X2 != sK12
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X0)) ),
inference(resolution_lifted,[status(thm)],[c_616,c_88]) ).
cnf(c_746,plain,
( ~ element(sK11,the_carrier(sK10))
| ~ element(sK12,the_carrier(sK10))
| ~ rel_str(sK10)
| in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),the_InternalRel(sK10)) ),
inference(unflattening,[status(thm)],[c_745]) ).
cnf(c_747,plain,
in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK12)),the_InternalRel(sK10)),
inference(global_subsumption_just,[status(thm)],[c_746,c_91,c_90,c_89,c_746]) ).
cnf(c_759,plain,
( X0 != sK10
| element(the_InternalRel(X0),powerset(cartesian_product2(the_carrier(X0),the_carrier(X0)))) ),
inference(resolution_lifted,[status(thm)],[c_708,c_91]) ).
cnf(c_760,plain,
element(the_InternalRel(sK10),powerset(cartesian_product2(the_carrier(sK10),the_carrier(sK10)))),
inference(unflattening,[status(thm)],[c_759]) ).
cnf(c_2125,plain,
relation(the_InternalRel(sK10)),
inference(superposition,[status(thm)],[c_760,c_50]) ).
cnf(c_2151,plain,
( in(sK12,the_carrier(sK10))
| empty(the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_89,c_93]) ).
cnf(c_2284,plain,
( ~ in(X0,the_InternalRel(sK10))
| element(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
inference(superposition,[status(thm)],[c_760,c_95]) ).
cnf(c_2320,plain,
( ~ empty(cartesian_product2(the_carrier(sK10),the_carrier(sK10)))
| ~ in(X0,the_InternalRel(sK10)) ),
inference(superposition,[status(thm)],[c_760,c_96]) ).
cnf(c_2436,plain,
( ~ in(X0,the_InternalRel(sK10))
| in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10)))
| empty(cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
inference(superposition,[status(thm)],[c_2284,c_93]) ).
cnf(c_2445,plain,
( in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10)))
| ~ in(X0,the_InternalRel(sK10)) ),
inference(global_subsumption_just,[status(thm)],[c_2436,c_2320,c_2436]) ).
cnf(c_2446,plain,
( ~ in(X0,the_InternalRel(sK10))
| in(X0,cartesian_product2(the_carrier(sK10),the_carrier(sK10))) ),
inference(renaming,[status(thm)],[c_2445]) ).
cnf(c_2455,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),the_InternalRel(sK10))
| in(X0,the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_2446,c_579]) ).
cnf(c_2473,plain,
in(sK11,the_carrier(sK10)),
inference(superposition,[status(thm)],[c_747,c_2455]) ).
cnf(c_2479,plain,
~ empty(the_carrier(sK10)),
inference(superposition,[status(thm)],[c_2473,c_98]) ).
cnf(c_2482,plain,
in(sK12,the_carrier(sK10)),
inference(backward_subsumption_resolution,[status(thm)],[c_2151,c_2479]) ).
cnf(c_2582,plain,
( ~ in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK11)),the_InternalRel(sK10))
| ~ is_antisymmetric_in(the_InternalRel(sK10),X0)
| ~ in(sK11,X0)
| ~ in(sK12,X0)
| ~ relation(the_InternalRel(sK10))
| sK11 = sK12 ),
inference(superposition,[status(thm)],[c_747,c_638]) ).
cnf(c_2587,plain,
( ~ in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK11)),the_InternalRel(sK10))
| ~ is_antisymmetric_in(the_InternalRel(sK10),X0)
| ~ in(sK11,X0)
| ~ in(sK12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2582,c_86,c_2125]) ).
cnf(c_2658,plain,
( ~ is_antisymmetric_in(the_InternalRel(sK10),X0)
| ~ in(sK11,X0)
| ~ in(sK12,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2587,c_91,c_90,c_89,c_739,c_2587]) ).
cnf(c_2667,plain,
( ~ in(sK11,the_carrier(sK10))
| ~ in(sK12,the_carrier(sK10)) ),
inference(superposition,[status(thm)],[c_730,c_2658]) ).
cnf(c_2668,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2667,c_2482,c_2473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU339+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n027.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 20:51:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.46 Running first-order theorem proving
% 0.21/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.40/1.17 % SZS status Started for theBenchmark.p
% 3.40/1.17 % SZS status Theorem for theBenchmark.p
% 3.40/1.17
% 3.40/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.40/1.17
% 3.40/1.17 ------ iProver source info
% 3.40/1.17
% 3.40/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.40/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.40/1.17 git: non_committed_changes: false
% 3.40/1.17 git: last_make_outside_of_git: false
% 3.40/1.17
% 3.40/1.17 ------ Parsing...
% 3.40/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.40/1.17
% 3.40/1.17 ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 1 sf_s rm: 6 0s sf_e pe_s pe_e
% 3.40/1.17
% 3.40/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.40/1.17
% 3.40/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.40/1.17 ------ Proving...
% 3.40/1.17 ------ Problem Properties
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17 clauses 42
% 3.40/1.17 conjectures 3
% 3.40/1.17 EPR 10
% 3.40/1.17 Horn 35
% 3.40/1.17 unary 21
% 3.40/1.17 binary 9
% 3.40/1.17 lits 79
% 3.40/1.17 lits eq 6
% 3.40/1.17 fd_pure 0
% 3.40/1.17 fd_pseudo 0
% 3.40/1.17 fd_cond 1
% 3.40/1.17 fd_pseudo_cond 2
% 3.40/1.17 AC symbols 0
% 3.40/1.17
% 3.40/1.17 ------ Schedule dynamic 5 is on
% 3.40/1.17
% 3.40/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17 ------
% 3.40/1.17 Current options:
% 3.40/1.17 ------
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17 ------ Proving...
% 3.40/1.17
% 3.40/1.17
% 3.40/1.17 % SZS status Theorem for theBenchmark.p
% 3.40/1.17
% 3.40/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.40/1.17
% 3.40/1.18
%------------------------------------------------------------------------------