TSTP Solution File: SEU265+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 17:05:19 EDT 2023
% Result : Theorem 3.85s 1.18s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 144 ( 21 unt; 0 def)
% Number of atoms : 426 ( 92 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 477 ( 195 ~; 211 |; 43 &)
% ( 8 <=>; 18 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 323 ( 14 sgn; 189 !; 46 ?)
% 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] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
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(f13,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f17,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] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f26,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(f30,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f33,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f35,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f36,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f38,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f46,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f47,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) )
<~> relation_dom_as_subset(X1,X0,X2) = X1 )
& relation_of2_as_subset(X2,X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f60,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK0(X0,X1),X4),X0)
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK0(X0,X1),X4),X0)
=> in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK2(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f63,f66,f65,f64]) ).
fof(f70,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f70]) ).
fof(f78,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,[],[f26]) ).
fof(f79,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f80,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X3] :
( ? [X4] : in(ordered_pair(X3,X4),X2)
| ~ in(X3,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1) ) )
& relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
( ? [X0,X1,X2] :
( ( relation_dom_as_subset(X1,X0,X2) != X1
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),X2)
& in(X3,X1) ) )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),X2)
| ~ in(X5,X1) ) )
& relation_of2_as_subset(X2,X1,X0) )
=> ( ( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),sK10)
& in(X3,sK9) ) )
& ( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),sK10)
| ~ in(X5,sK9) ) )
& relation_of2_as_subset(sK10,sK9,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ? [X3] :
( ! [X4] : ~ in(ordered_pair(X3,X4),sK10)
& in(X3,sK9) )
=> ( ! [X4] : ~ in(ordered_pair(sK11,X4),sK10)
& in(sK11,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X5] :
( ? [X6] : in(ordered_pair(X5,X6),sK10)
=> in(ordered_pair(X5,sK12(X5)),sK10) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ( ! [X4] : ~ in(ordered_pair(sK11,X4),sK10)
& in(sK11,sK9) ) )
& ( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| ! [X5] :
( in(ordered_pair(X5,sK12(X5)),sK10)
| ~ in(X5,sK9) ) )
& relation_of2_as_subset(sK10,sK9,sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f81,f84,f83,f82]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f87,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) )
& ( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) )
& ( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f86,f87]) ).
fof(f90,plain,
! [X2,X0,X1] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f43]) ).
fof(f91,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f92,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f93,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f94,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f96,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f97,plain,
! [X2,X0,X1] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f98,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f100,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f71]) ).
fof(f106,plain,
! [X2,X0,X1] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f107,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
relation_of2_as_subset(sK10,sK9,sK8),
inference(cnf_transformation,[],[f85]) ).
fof(f114,plain,
! [X5] :
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| in(ordered_pair(X5,sK12(X5)),sK10)
| ~ in(X5,sK9) ),
inference(cnf_transformation,[],[f85]) ).
fof(f115,plain,
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| in(sK11,sK9) ),
inference(cnf_transformation,[],[f85]) ).
fof(f116,plain,
! [X4] :
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(ordered_pair(sK11,X4),sK10) ),
inference(cnf_transformation,[],[f85]) ).
fof(f117,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f118,plain,
! [X0,X1] :
( X0 = X1
| in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f119,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f121,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f124,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f127,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f94,f96]) ).
fof(f128,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f93,f96]) ).
fof(f129,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f92,f96]) ).
fof(f133,plain,
! [X4] :
( sK9 != relation_dom_as_subset(sK9,sK8,sK10)
| ~ in(unordered_pair(unordered_pair(sK11,X4),singleton(sK11)),sK10) ),
inference(definition_unfolding,[],[f116,f96]) ).
fof(f134,plain,
! [X5] :
( sK9 = relation_dom_as_subset(sK9,sK8,sK10)
| in(unordered_pair(unordered_pair(X5,sK12(X5)),singleton(X5)),sK10)
| ~ in(X5,sK9) ),
inference(definition_unfolding,[],[f114,f96]) ).
fof(f135,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f136,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f129]) ).
cnf(c_50,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f91]) ).
cnf(c_53,plain,
( ~ relation(X0)
| relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_54,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_55,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK2(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_56,plain,
( ~ relation_of2(X0,X1,X2)
| element(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_57,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_59,plain,
element(sK4(X0),X0),
inference(cnf_transformation,[],[f100]) ).
cnf(c_65,plain,
( ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_67,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_72,negated_conjecture,
( relation_dom_as_subset(sK9,sK8,sK10) != sK9
| ~ in(unordered_pair(unordered_pair(sK11,X0),singleton(sK11)),sK10) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_73,negated_conjecture,
( relation_dom_as_subset(sK9,sK8,sK10) != sK9
| in(sK11,sK9) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_74,negated_conjecture,
( ~ in(X0,sK9)
| relation_dom_as_subset(sK9,sK8,sK10) = sK9
| in(unordered_pair(unordered_pair(X0,sK12(X0)),singleton(X0)),sK10) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_75,negated_conjecture,
relation_of2_as_subset(sK10,sK9,sK8),
inference(cnf_transformation,[],[f113]) ).
cnf(c_76,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_77,plain,
( ~ in(sK13(X0,X1),X0)
| ~ in(sK13(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_78,plain,
( X0 = X1
| in(sK13(X0,X1),X0)
| in(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_80,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_81,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_83,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_126,plain,
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
cnf(c_127,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(renaming,[status(thm)],[c_126]) ).
cnf(c_132,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_67,c_56]) ).
cnf(c_134,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(prop_impl_just,[status(thm)],[c_67,c_65]) ).
cnf(c_136,plain,
( relation_dom_as_subset(sK9,sK8,sK10) != sK9
| ~ in(unordered_pair(unordered_pair(sK11,X0),singleton(sK11)),sK10) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
cnf(c_138,plain,
( relation_dom_as_subset(sK9,sK8,sK10) != sK9
| in(sK11,sK9) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
cnf(c_459,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(demodulation,[status(thm)],[c_54,c_51]) ).
cnf(c_466,plain,
( relation_dom_as_subset(sK9,sK8,sK10) != sK9
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK10) ),
inference(demodulation,[status(thm)],[c_136,c_51]) ).
cnf(c_471,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK2(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_55,c_51]) ).
cnf(c_478,plain,
( ~ in(X0,sK9)
| relation_dom_as_subset(sK9,sK8,sK10) = sK9
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK12(X0))),sK10) ),
inference(demodulation,[status(thm)],[c_74,c_51]) ).
cnf(c_485,plain,
( ~ relation(X0)
| relation_dom(X0) = X1
| in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| in(sK0(X0,X1),X1) ),
inference(demodulation,[status(thm)],[c_53,c_51]) ).
cnf(c_556,plain,
( X0 != sK10
| X1 != sK9
| X2 != sK8
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(resolution_lifted,[status(thm)],[c_134,c_75]) ).
cnf(c_557,plain,
relation_dom_as_subset(sK9,sK8,sK10) = relation_dom(sK10),
inference(unflattening,[status(thm)],[c_556]) ).
cnf(c_561,plain,
( X0 != sK10
| X1 != sK9
| X2 != sK8
| element(relation_dom_as_subset(X1,X2,X0),powerset(X1)) ),
inference(resolution_lifted,[status(thm)],[c_132,c_75]) ).
cnf(c_562,plain,
element(relation_dom_as_subset(sK9,sK8,sK10),powerset(sK9)),
inference(unflattening,[status(thm)],[c_561]) ).
cnf(c_566,plain,
( X0 != sK10
| X1 != sK9
| X2 != sK8
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(resolution_lifted,[status(thm)],[c_127,c_75]) ).
cnf(c_567,plain,
element(sK10,powerset(cartesian_product2(sK9,sK8))),
inference(unflattening,[status(thm)],[c_566]) ).
cnf(c_827,plain,
element(relation_dom(sK10),powerset(sK9)),
inference(demodulation,[status(thm)],[c_562,c_557]) ).
cnf(c_848,plain,
( relation_dom(sK10) != sK9
| in(sK11,sK9) ),
inference(light_normalisation,[status(thm)],[c_138,c_557]) ).
cnf(c_891,plain,
( relation_dom(sK10) != sK9
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK10) ),
inference(light_normalisation,[status(thm)],[c_466,c_557]) ).
cnf(c_902,plain,
( ~ in(X0,sK9)
| relation_dom(sK10) = sK9
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK12(X0))),sK10) ),
inference(light_normalisation,[status(thm)],[c_478,c_557]) ).
cnf(c_1466,plain,
( ~ in(X0,sK9)
| ~ empty(sK10)
| relation_dom(sK10) = sK9 ),
inference(superposition,[status(thm)],[c_902,c_83]) ).
cnf(c_1505,plain,
relation(sK10),
inference(superposition,[status(thm)],[c_567,c_50]) ).
cnf(c_1519,plain,
( in(sK4(X0),X0)
| empty(X0) ),
inference(superposition,[status(thm)],[c_59,c_76]) ).
cnf(c_1563,plain,
( ~ in(X0,relation_dom(sK10))
| element(X0,sK9) ),
inference(superposition,[status(thm)],[c_827,c_80]) ).
cnf(c_1667,plain,
( ~ in(X0,relation_dom(sK10))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_827,c_81]) ).
cnf(c_1699,plain,
( relation_dom(sK10) = X0
| in(sK13(X0,relation_dom(sK10)),X0)
| element(sK13(X0,relation_dom(sK10)),sK9) ),
inference(superposition,[status(thm)],[c_78,c_1563]) ).
cnf(c_1742,plain,
( ~ in(sK11,sK9)
| ~ empty(sK9) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_1785,plain,
( ~ in(X0,sK9)
| ~ relation(sK10)
| relation_dom(sK10) = sK9
| in(X0,relation_dom(sK10)) ),
inference(superposition,[status(thm)],[c_902,c_459]) ).
cnf(c_1792,plain,
( ~ in(X0,sK9)
| relation_dom(sK10) = sK9
| in(X0,relation_dom(sK10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1785,c_1505]) ).
cnf(c_1855,plain,
( ~ empty(sK9)
| relation_dom(sK10) = X0
| in(sK13(X0,relation_dom(sK10)),X0) ),
inference(superposition,[status(thm)],[c_78,c_1667]) ).
cnf(c_1857,plain,
( ~ empty(sK9)
| empty(relation_dom(sK10)) ),
inference(superposition,[status(thm)],[c_1519,c_1667]) ).
cnf(c_1867,plain,
( ~ empty(sK9)
| relation_dom(sK10) = sK9
| in(sK13(sK9,relation_dom(sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_1855]) ).
cnf(c_1906,plain,
( ~ in(sK13(X0,relation_dom(sK10)),X0)
| ~ in(sK13(X0,relation_dom(sK10)),sK9)
| relation_dom(sK10) = X0
| relation_dom(sK10) = sK9 ),
inference(superposition,[status(thm)],[c_1792,c_77]) ).
cnf(c_1948,plain,
( ~ in(sK13(sK9,relation_dom(sK10)),sK9)
| relation_dom(sK10) = sK9 ),
inference(instantiation,[status(thm)],[c_1906]) ).
cnf(c_1981,plain,
~ empty(sK9),
inference(global_subsumption_just,[status(thm)],[c_1857,c_848,c_1742,c_1867,c_1948]) ).
cnf(c_2055,plain,
( ~ relation(sK9)
| ~ empty(sK10)
| relation_dom(sK9) = X0
| relation_dom(sK10) = sK9
| in(sK0(sK9,X0),X0) ),
inference(superposition,[status(thm)],[c_485,c_1466]) ).
cnf(c_2644,plain,
( relation_dom(sK10) = X0
| in(sK13(X0,relation_dom(sK10)),X0)
| in(sK13(X0,relation_dom(sK10)),sK9)
| empty(sK9) ),
inference(superposition,[status(thm)],[c_1699,c_76]) ).
cnf(c_2673,plain,
( relation_dom(sK10) = X0
| in(sK13(X0,relation_dom(sK10)),X0)
| in(sK13(X0,relation_dom(sK10)),sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2644,c_1981]) ).
cnf(c_2686,plain,
( relation_dom(sK10) = sK9
| in(sK13(sK9,relation_dom(sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_2673]) ).
cnf(c_2820,plain,
relation_dom(sK10) = sK9,
inference(global_subsumption_just,[status(thm)],[c_2055,c_1948,c_2686]) ).
cnf(c_2846,plain,
( sK9 != sK9
| ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK10) ),
inference(demodulation,[status(thm)],[c_891,c_2820]) ).
cnf(c_2847,plain,
( sK9 != sK9
| in(sK11,sK9) ),
inference(demodulation,[status(thm)],[c_848,c_2820]) ).
cnf(c_2856,plain,
in(sK11,sK9),
inference(equality_resolution_simp,[status(thm)],[c_2847]) ).
cnf(c_2857,plain,
~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X0)),sK10),
inference(equality_resolution_simp,[status(thm)],[c_2846]) ).
cnf(c_2908,plain,
( ~ in(sK11,relation_dom(sK10))
| ~ relation(sK10) ),
inference(superposition,[status(thm)],[c_471,c_2857]) ).
cnf(c_2911,plain,
( ~ in(sK11,sK9)
| ~ relation(sK10) ),
inference(light_normalisation,[status(thm)],[c_2908,c_2820]) ).
cnf(c_2912,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2911,c_1505,c_2856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU265+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.18/0.35 % Computer : n022.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Wed Aug 23 20:14:11 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.85/1.18 % SZS status Started for theBenchmark.p
% 3.85/1.18 % SZS status Theorem for theBenchmark.p
% 3.85/1.18
% 3.85/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.85/1.18
% 3.85/1.18 ------ iProver source info
% 3.85/1.18
% 3.85/1.18 git: date: 2023-05-31 18:12:56 +0000
% 3.85/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.85/1.18 git: non_committed_changes: false
% 3.85/1.18 git: last_make_outside_of_git: false
% 3.85/1.18
% 3.85/1.18 ------ Parsing...
% 3.85/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.85/1.18
% 3.85/1.18 ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 6 sf_s rm: 3 0s sf_e pe_s pe_e
% 3.85/1.18
% 3.85/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.85/1.18
% 3.85/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.85/1.18 ------ Proving...
% 3.85/1.18 ------ Problem Properties
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18 clauses 35
% 3.85/1.18 conjectures 0
% 3.85/1.18 EPR 9
% 3.85/1.18 Horn 31
% 3.85/1.18 unary 16
% 3.85/1.18 binary 7
% 3.85/1.18 lits 68
% 3.85/1.18 lits eq 13
% 3.85/1.18 fd_pure 0
% 3.85/1.18 fd_pseudo 0
% 3.85/1.18 fd_cond 1
% 3.85/1.18 fd_pseudo_cond 5
% 3.85/1.18 AC symbols 0
% 3.85/1.18
% 3.85/1.18 ------ Schedule dynamic 5 is on
% 3.85/1.18
% 3.85/1.18 ------ no conjectures: strip conj schedule
% 3.85/1.18
% 3.85/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18 ------
% 3.85/1.18 Current options:
% 3.85/1.18 ------
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18 ------ Proving...
% 3.85/1.18
% 3.85/1.18
% 3.85/1.18 % SZS status Theorem for theBenchmark.p
% 3.85/1.18
% 3.85/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.18
% 3.85/1.18
%------------------------------------------------------------------------------