TSTP Solution File: SEU190+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU190+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 03:04:55 EDT 2024
% Result : Theorem 9.84s 2.20s
% Output : CNFRefutation 9.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f14,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f32,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f34,conjecture,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
inference(negated_conjecture,[],[f34]) ).
fof(f40,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f54,plain,
? [X0] :
( relation_rng(identity_relation(X0)) != X0
| relation_dom(identity_relation(X0)) != X0 ),
inference(ennf_transformation,[],[f35]) ).
fof(f57,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f40]) ).
fof(f58,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( ( sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( sK0(X0,X1) = sK1(X0,X1)
& in(sK0(X0,X1),X0) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f59,f60]) ).
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,[],[f41]) ).
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(sK2(X0,X1),X3),X0)
| ~ in(sK2(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK2(X0,X1),X4),X0)
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK2(X0,X1),X4),X0)
=> in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK4(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK2(X0,X1),X3),X0)
| ~ in(sK2(X0,X1),X1) )
& ( in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK4(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f63,f66,f65,f64]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
=> in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK7(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f69,f72,f71,f70]) ).
fof(f84,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f85,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(f86,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])],[f84,f85]) ).
fof(f87,plain,
( ? [X0] :
( relation_rng(identity_relation(X0)) != X0
| relation_dom(identity_relation(X0)) != X0 )
=> ( sK14 != relation_rng(identity_relation(sK14))
| sK14 != relation_dom(identity_relation(sK14)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( sK14 != relation_rng(identity_relation(sK14))
| sK14 != relation_dom(identity_relation(sK14)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f54,f87]) ).
fof(f91,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f92,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f94,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f98,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK4(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f99,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(f102,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f103,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f106,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f107,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f129,plain,
! [X0,X1] :
( X0 = X1
| in(sK13(X0,X1),X1)
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f130,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f132,plain,
( sK14 != relation_rng(identity_relation(sK14))
| sK14 != relation_dom(identity_relation(sK14)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f138,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f94,f106]) ).
fof(f139,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f93,f106]) ).
fof(f140,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f92,f106]) ).
fof(f143,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,[],[f99,f106]) ).
fof(f144,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f98,f106]) ).
fof(f147,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f103,f106]) ).
fof(f148,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f102,f106]) ).
fof(f150,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f151,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),singleton(X5)),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f150]) ).
fof(f152,plain,
! [X0,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f139]) ).
fof(f153,plain,
! [X0,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f140]) ).
fof(f154,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f143]) ).
fof(f155,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK4(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f156,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f147]) ).
fof(f157,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK7(X0,X5),X5),singleton(sK7(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f148]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f91]) ).
cnf(c_55,plain,
( ~ in(X0,X1)
| ~ relation(identity_relation(X1))
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1)) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_56,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2))
| ~ relation(identity_relation(X2))
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_57,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2))
| ~ relation(identity_relation(X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_60,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_61,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK4(X1,X0)),singleton(X0)),X1) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_64,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_65,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK7(X1,X0),X0),singleton(sK7(X1,X0))),X1) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_66,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f107]) ).
cnf(c_88,plain,
( ~ in(sK13(X0,X1),X0)
| ~ in(sK13(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_89,plain,
( X0 = X1
| in(sK13(X0,X1),X0)
| in(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_91,negated_conjecture,
( relation_dom(identity_relation(sK14)) != sK14
| relation_rng(identity_relation(sK14)) != sK14 ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_137,plain,
( ~ in(X0,X1)
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),identity_relation(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_55,c_66]) ).
cnf(c_138,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2))
| in(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_66]) ).
cnf(c_139,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),identity_relation(X2))
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_66]) ).
cnf(c_382,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2))
| in(X0,X2) ),
inference(demodulation,[status(thm)],[c_138,c_51]) ).
cnf(c_387,plain,
( ~ in(X0,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),identity_relation(X1)) ),
inference(demodulation,[status(thm)],[c_137,c_51]) ).
cnf(c_392,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),identity_relation(X2))
| X0 = X1 ),
inference(demodulation,[status(thm)],[c_139,c_51]) ).
cnf(c_413,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(demodulation,[status(thm)],[c_64,c_51]) ).
cnf(c_420,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(demodulation,[status(thm)],[c_60,c_51]) ).
cnf(c_427,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK4(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_61,c_51]) ).
cnf(c_434,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(sK7(X1,X0)),unordered_pair(X0,sK7(X1,X0))),X1) ),
inference(demodulation,[status(thm)],[c_65,c_51]) ).
cnf(c_2848,plain,
identity_relation(sK14) = sP0_iProver_def,
definition ).
cnf(c_2849,plain,
relation_dom(sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_2850,plain,
relation_rng(sP0_iProver_def) = sP2_iProver_def,
definition ).
cnf(c_2851,negated_conjecture,
( sP1_iProver_def != sK14
| sP2_iProver_def != sK14 ),
inference(demodulation,[status(thm)],[c_91,c_2850,c_2848,c_2849]) ).
cnf(c_2852,plain,
X0 = X0,
theory(equality) ).
cnf(c_2854,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3781,plain,
( ~ in(sK13(sP1_iProver_def,sK14),sK14)
| ~ in(sK13(sP1_iProver_def,sK14),sP1_iProver_def)
| sP1_iProver_def = sK14 ),
inference(instantiation,[status(thm)],[c_88]) ).
cnf(c_4856,plain,
( X0 != X1
| sK14 != X1
| sK14 = X0 ),
inference(instantiation,[status(thm)],[c_2854]) ).
cnf(c_7805,plain,
( X0 != sK14
| sK14 != sK14
| sK14 = X0 ),
inference(instantiation,[status(thm)],[c_4856]) ).
cnf(c_7806,plain,
sK14 = sK14,
inference(instantiation,[status(thm)],[c_2852]) ).
cnf(c_14859,plain,
( sK14 != sK14
| sP1_iProver_def != sK14
| sK14 = sP1_iProver_def ),
inference(instantiation,[status(thm)],[c_7805]) ).
cnf(c_21355,plain,
relation(sP0_iProver_def),
inference(superposition,[status(thm)],[c_2848,c_66]) ).
cnf(c_21714,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sP0_iProver_def)
| X0 = X1 ),
inference(superposition,[status(thm)],[c_2848,c_392]) ).
cnf(c_21739,plain,
( ~ in(X0,X1)
| ~ relation(identity_relation(X1))
| in(X0,relation_rng(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_387,c_413]) ).
cnf(c_21742,plain,
( ~ in(X0,X1)
| in(X0,relation_rng(identity_relation(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21739,c_66]) ).
cnf(c_21754,plain,
( ~ in(X0,X1)
| ~ relation(identity_relation(X1))
| in(X0,relation_dom(identity_relation(X1))) ),
inference(superposition,[status(thm)],[c_387,c_420]) ).
cnf(c_21755,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(superposition,[status(thm)],[c_51,c_420]) ).
cnf(c_21757,plain,
( ~ in(X0,X1)
| in(X0,relation_dom(identity_relation(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21754,c_66]) ).
cnf(c_21783,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sP0_iProver_def)
| X0 = X1 ),
inference(superposition,[status(thm)],[c_51,c_21714]) ).
cnf(c_21807,plain,
( ~ in(X0,sK14)
| in(X0,relation_rng(sP0_iProver_def)) ),
inference(superposition,[status(thm)],[c_2848,c_21742]) ).
cnf(c_21815,plain,
( ~ in(X0,sK14)
| in(X0,sP2_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_21807,c_2850]) ).
cnf(c_21845,plain,
( X0 = sK14
| in(sK13(sK14,X0),X0)
| in(sK13(sK14,X0),sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_89,c_21815]) ).
cnf(c_21876,plain,
( ~ in(X0,sK14)
| in(X0,relation_dom(sP0_iProver_def)) ),
inference(superposition,[status(thm)],[c_2848,c_21757]) ).
cnf(c_21884,plain,
( ~ in(X0,sK14)
| in(X0,sP1_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_21876,c_2849]) ).
cnf(c_21913,plain,
( X0 = sK14
| in(sK13(X0,sK14),X0)
| in(sK13(X0,sK14),sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_89,c_21884]) ).
cnf(c_21951,plain,
( ~ in(X0,relation_dom(identity_relation(X1)))
| ~ relation(identity_relation(X1))
| in(X0,X1) ),
inference(superposition,[status(thm)],[c_427,c_382]) ).
cnf(c_21963,plain,
( ~ in(X0,relation_dom(identity_relation(X1)))
| in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21951,c_66]) ).
cnf(c_21998,plain,
( ~ in(X0,relation_rng(sP0_iProver_def))
| ~ relation(sP0_iProver_def)
| sK7(sP0_iProver_def,X0) = X0 ),
inference(superposition,[status(thm)],[c_434,c_21783]) ).
cnf(c_22005,plain,
( ~ in(X0,sP2_iProver_def)
| ~ relation(sP0_iProver_def)
| sK7(sP0_iProver_def,X0) = X0 ),
inference(light_normalisation,[status(thm)],[c_21998,c_2850]) ).
cnf(c_22006,plain,
( ~ in(X0,sP2_iProver_def)
| sK7(sP0_iProver_def,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_22005,c_21355]) ).
cnf(c_22232,plain,
( ~ in(X0,relation_dom(sP0_iProver_def))
| in(X0,sK14) ),
inference(superposition,[status(thm)],[c_2848,c_21963]) ).
cnf(c_22233,plain,
( ~ in(X0,sP1_iProver_def)
| in(X0,sK14) ),
inference(light_normalisation,[status(thm)],[c_22232,c_2849]) ).
cnf(c_23731,plain,
( sK14 = sP2_iProver_def
| in(sK13(sK14,sP2_iProver_def),sP2_iProver_def) ),
inference(equality_factoring,[status(thm)],[c_21845]) ).
cnf(c_23994,plain,
( ~ in(sK13(sK14,sP2_iProver_def),sK14)
| sK14 = sP2_iProver_def ),
inference(superposition,[status(thm)],[c_23731,c_88]) ).
cnf(c_34557,plain,
( sK14 = sP1_iProver_def
| in(sK13(sP1_iProver_def,sK14),sP1_iProver_def) ),
inference(equality_factoring,[status(thm)],[c_21913]) ).
cnf(c_36642,plain,
( sK14 = sP1_iProver_def
| in(sK13(sP1_iProver_def,sK14),sK14) ),
inference(superposition,[status(thm)],[c_34557,c_22233]) ).
cnf(c_36649,plain,
sK14 = sP1_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_36642,c_3781,c_7806,c_14859,c_34557,c_36642]) ).
cnf(c_36654,plain,
( ~ in(sK13(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def)
| sP1_iProver_def = sP2_iProver_def ),
inference(demodulation,[status(thm)],[c_23994,c_36649]) ).
cnf(c_36659,plain,
( sP1_iProver_def = sP2_iProver_def
| in(sK13(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
inference(demodulation,[status(thm)],[c_23731,c_36649]) ).
cnf(c_36714,plain,
( sP1_iProver_def != sP1_iProver_def
| sP1_iProver_def != sP2_iProver_def ),
inference(demodulation,[status(thm)],[c_2851,c_36649]) ).
cnf(c_36729,plain,
sP1_iProver_def != sP2_iProver_def,
inference(equality_resolution_simp,[status(thm)],[c_36714]) ).
cnf(c_36731,plain,
in(sK13(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_36659,c_36729]) ).
cnf(c_36736,plain,
~ in(sK13(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_36654,c_36729]) ).
cnf(c_36760,plain,
sK7(sP0_iProver_def,sK13(sP1_iProver_def,sP2_iProver_def)) = sK13(sP1_iProver_def,sP2_iProver_def),
inference(superposition,[status(thm)],[c_36731,c_22006]) ).
cnf(c_38087,plain,
( ~ in(sK13(sP1_iProver_def,sP2_iProver_def),relation_rng(sP0_iProver_def))
| ~ relation(sP0_iProver_def)
| in(unordered_pair(singleton(sK13(sP1_iProver_def,sP2_iProver_def)),unordered_pair(sK13(sP1_iProver_def,sP2_iProver_def),sK13(sP1_iProver_def,sP2_iProver_def))),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_36760,c_434]) ).
cnf(c_38088,plain,
( ~ in(sK13(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def)
| ~ relation(sP0_iProver_def)
| in(unordered_pair(singleton(sK13(sP1_iProver_def,sP2_iProver_def)),unordered_pair(sK13(sP1_iProver_def,sP2_iProver_def),sK13(sP1_iProver_def,sP2_iProver_def))),sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_38087,c_2850]) ).
cnf(c_38089,plain,
in(unordered_pair(singleton(sK13(sP1_iProver_def,sP2_iProver_def)),unordered_pair(sK13(sP1_iProver_def,sP2_iProver_def),sK13(sP1_iProver_def,sP2_iProver_def))),sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_38088,c_21355,c_36731]) ).
cnf(c_38127,plain,
( ~ relation(sP0_iProver_def)
| in(sK13(sP1_iProver_def,sP2_iProver_def),relation_dom(sP0_iProver_def)) ),
inference(superposition,[status(thm)],[c_38089,c_21755]) ).
cnf(c_38131,plain,
( ~ relation(sP0_iProver_def)
| in(sK13(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_38127,c_2849]) ).
cnf(c_38132,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_38131,c_36736,c_21355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU190+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 17:42:25 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.84/2.20 % SZS status Started for theBenchmark.p
% 9.84/2.20 % SZS status Theorem for theBenchmark.p
% 9.84/2.20
% 9.84/2.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 9.84/2.20
% 9.84/2.20 ------ iProver source info
% 9.84/2.20
% 9.84/2.20 git: date: 2024-05-02 19:28:25 +0000
% 9.84/2.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 9.84/2.20 git: non_committed_changes: false
% 9.84/2.20
% 9.84/2.20 ------ Parsing...
% 9.84/2.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.84/2.20
% 9.84/2.20 ------ Preprocessing... sup_sim: 14 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 9.84/2.20
% 9.84/2.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.84/2.20
% 9.84/2.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.84/2.20 ------ Proving...
% 9.84/2.20 ------ Problem Properties
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20 clauses 44
% 9.84/2.20 conjectures 1
% 9.84/2.20 EPR 14
% 9.84/2.20 Horn 38
% 9.84/2.20 unary 15
% 9.84/2.20 binary 13
% 9.84/2.20 lits 97
% 9.84/2.20 lits eq 20
% 9.84/2.20 fd_pure 0
% 9.84/2.20 fd_pseudo 0
% 9.84/2.20 fd_cond 1
% 9.84/2.20 fd_pseudo_cond 11
% 9.84/2.20 AC symbols 0
% 9.84/2.20
% 9.84/2.20 ------ Schedule dynamic 5 is on
% 9.84/2.20
% 9.84/2.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20 ------
% 9.84/2.20 Current options:
% 9.84/2.20 ------
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20 ------ Proving...
% 9.84/2.20
% 9.84/2.20
% 9.84/2.20 % SZS status Theorem for theBenchmark.p
% 9.84/2.20
% 9.84/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.84/2.21
% 9.84/2.21
%------------------------------------------------------------------------------