TSTP Solution File: SEU181+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU181+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 17:04:27 EDT 2023
% Result : Theorem 35.66s 5.74s
% Output : CNFRefutation 35.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 96 ( 8 unt; 0 def)
% Number of atoms : 399 ( 71 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 517 ( 214 ~; 232 |; 42 &)
% ( 12 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-2 aty)
% Number of variables : 242 ( 3 sgn; 172 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,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(f22,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(f24,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(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f44,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f102,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f115,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f116,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(negated_conjecture,[],[f115]) ).
fof(f143,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f177,plain,
! [X0] :
( ! [X1] :
( ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f182,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f102]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f223]) ).
fof(f237,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(relation_inverse(X0))
| relation_rng(X0) != relation_dom(relation_inverse(X0)) )
& relation(X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f322,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,[],[f173]) ).
fof(f323,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,[],[f322]) ).
fof(f324,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(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK18(X0,X1),X4),X0)
| in(sK18(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK18(X0,X1),X4),X0)
=> in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK20(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f323,f326,f325,f324]) ).
fof(f339,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,[],[f174]) ).
fof(f340,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,[],[f339]) ).
fof(f341,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,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK25(X0,X1)),X0)
=> in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK27(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1) )
& ( in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f340,f343,f342,f341]) ).
fof(f345,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f346,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f345]) ).
fof(f347,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( ~ in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| ~ in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1) )
& ( in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| ~ in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1) )
& ( in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f346,f347]) ).
fof(f383,plain,
( ? [X0] :
( ( relation_dom(X0) != relation_rng(relation_inverse(X0))
| relation_rng(X0) != relation_dom(relation_inverse(X0)) )
& relation(X0) )
=> ( ( relation_dom(sK40) != relation_rng(relation_inverse(sK40))
| relation_rng(sK40) != relation_dom(relation_inverse(sK40)) )
& relation(sK40) ) ),
introduced(choice_axiom,[]) ).
fof(f384,plain,
( ( relation_dom(sK40) != relation_rng(relation_inverse(sK40))
| relation_rng(sK40) != relation_dom(relation_inverse(sK40)) )
& relation(sK40) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f237,f383]) ).
fof(f465,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f467,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| in(sK18(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f468,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f482,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f344]) ).
fof(f484,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f344]) ).
fof(f485,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f344]) ).
fof(f487,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f489,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f490,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f503,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f573,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f224]) ).
fof(f574,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f224]) ).
fof(f591,plain,
relation(sK40),
inference(cnf_transformation,[],[f384]) ).
fof(f592,plain,
( relation_dom(sK40) != relation_rng(relation_inverse(sK40))
| relation_rng(sK40) != relation_dom(relation_inverse(sK40)) ),
inference(cnf_transformation,[],[f384]) ).
fof(f631,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f143]) ).
fof(f648,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f487,f631]) ).
fof(f666,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK18(X0,X1),X3),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| ~ in(sK18(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f468,f648]) ).
fof(f667,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK18(X0,X1),sK19(X0,X1)),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| in(sK18(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f467,f648]) ).
fof(f669,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f465,f648]) ).
fof(f670,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK25(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f485,f648]) ).
fof(f671,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| in(sK25(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f484,f648]) ).
fof(f673,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f482,f648]) ).
fof(f676,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f490,f648,f648]) ).
fof(f677,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f489,f648,f648]) ).
fof(f702,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f574,f648]) ).
fof(f703,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f573,f648]) ).
fof(f756,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK20(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f669]) ).
fof(f764,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK27(X0,X5),X5),unordered_pair(sK27(X0,X5),sK27(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f673]) ).
fof(f765,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f676]) ).
fof(f766,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f677]) ).
cnf(c_111,plain,
( ~ in(unordered_pair(unordered_pair(sK18(X0,X1),X2),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| ~ in(sK18(X0,X1),X1)
| ~ relation(X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f666]) ).
cnf(c_112,plain,
( ~ relation(X0)
| relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK18(X0,X1),sK19(X0,X1)),unordered_pair(sK18(X0,X1),sK18(X0,X1))),X0)
| in(sK18(X0,X1),X1) ),
inference(cnf_transformation,[],[f667]) ).
cnf(c_114,plain,
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X0,sK20(X1,X0)),unordered_pair(X0,X0)),X1) ),
inference(cnf_transformation,[],[f756]) ).
cnf(c_128,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK25(X1,X2)),unordered_pair(X0,X0)),X1)
| ~ in(sK25(X1,X2),X2)
| ~ relation(X1)
| relation_rng(X1) = X2 ),
inference(cnf_transformation,[],[f670]) ).
cnf(c_129,plain,
( ~ relation(X0)
| relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK26(X0,X1),sK26(X0,X1))),X0)
| in(sK25(X0,X1),X1) ),
inference(cnf_transformation,[],[f671]) ).
cnf(c_131,plain,
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK27(X1,X0),X0),unordered_pair(sK27(X1,X0),sK27(X1,X0))),X1) ),
inference(cnf_transformation,[],[f764]) ).
cnf(c_136,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f765]) ).
cnf(c_137,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2))
| ~ relation(relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2) ),
inference(cnf_transformation,[],[f766]) ).
cnf(c_148,plain,
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f503]) ).
cnf(c_218,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f702]) ).
cnf(c_219,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f703]) ).
cnf(c_236,negated_conjecture,
( relation_dom(relation_inverse(sK40)) != relation_rng(sK40)
| relation_rng(relation_inverse(sK40)) != relation_dom(sK40) ),
inference(cnf_transformation,[],[f592]) ).
cnf(c_237,negated_conjecture,
relation(sK40),
inference(cnf_transformation,[],[f591]) ).
cnf(c_506,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_136,c_148]) ).
cnf(c_507,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_inverse(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_137,c_148]) ).
cnf(c_3699,plain,
( ~ relation(sK40)
| relation(relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_148]) ).
cnf(c_4610,plain,
( ~ relation(relation_inverse(sK40))
| relation_dom(relation_inverse(sK40)) = relation_rng(sK40)
| in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40)) ),
inference(instantiation,[status(thm)],[c_112]) ).
cnf(c_4848,plain,
( ~ relation(relation_inverse(sK40))
| relation_rng(relation_inverse(sK40)) = relation_dom(sK40)
| in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40)))),relation_inverse(sK40))
| in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40)) ),
inference(instantiation,[status(thm)],[c_129]) ).
cnf(c_4956,plain,
( ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),X0),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ relation(relation_inverse(sK40))
| relation_dom(relation_inverse(sK40)) = relation_rng(sK40) ),
inference(instantiation,[status(thm)],[c_111]) ).
cnf(c_6262,plain,
( ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))))),sK40) ),
inference(instantiation,[status(thm)],[c_131]) ).
cnf(c_7566,plain,
( ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_507]) ).
cnf(c_9240,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(X0,X0)),sK40)
| ~ relation(sK40)
| in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40)) ),
inference(instantiation,[status(thm)],[c_218]) ).
cnf(c_12270,plain,
( ~ in(unordered_pair(unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK19(relation_inverse(sK40),relation_rng(sK40)),sK19(relation_inverse(sK40),relation_rng(sK40)))),sK40)
| ~ relation(sK40)
| in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40)) ),
inference(instantiation,[status(thm)],[c_9240]) ).
cnf(c_13852,plain,
( ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40)))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_114]) ).
cnf(c_19176,plain,
( ~ in(unordered_pair(unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK18(relation_inverse(sK40),relation_rng(sK40))),unordered_pair(sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40))))),sK40)
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40)))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_506]) ).
cnf(c_20362,plain,
( ~ in(unordered_pair(unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK26(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40)))),relation_inverse(sK40))
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40) ),
inference(instantiation,[status(thm)],[c_507]) ).
cnf(c_23052,plain,
( ~ in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK26(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40)
| ~ relation(sK40)
| in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40)) ),
inference(instantiation,[status(thm)],[c_219]) ).
cnf(c_31293,plain,
( ~ in(unordered_pair(unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK27(sK40,sK18(relation_inverse(sK40),relation_rng(sK40)))),unordered_pair(sK18(relation_inverse(sK40),relation_rng(sK40)),sK18(relation_inverse(sK40),relation_rng(sK40)))),relation_inverse(sK40))
| ~ in(sK18(relation_inverse(sK40),relation_rng(sK40)),relation_rng(sK40))
| ~ relation(relation_inverse(sK40))
| relation_dom(relation_inverse(sK40)) = relation_rng(sK40) ),
inference(instantiation,[status(thm)],[c_4956]) ).
cnf(c_33549,plain,
( ~ in(unordered_pair(unordered_pair(X0,sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(X0,X0)),relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ relation(relation_inverse(sK40))
| relation_rng(relation_inverse(sK40)) = relation_dom(sK40) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_38646,plain,
( ~ in(unordered_pair(unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40)))),unordered_pair(sK25(relation_inverse(sK40),relation_dom(sK40)),sK25(relation_inverse(sK40),relation_dom(sK40)))),sK40)
| ~ relation(sK40)
| in(unordered_pair(unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40)) ),
inference(instantiation,[status(thm)],[c_506]) ).
cnf(c_39714,plain,
( ~ in(unordered_pair(unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK25(relation_inverse(sK40),relation_dom(sK40))),unordered_pair(sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))),sK20(sK40,sK25(relation_inverse(sK40),relation_dom(sK40))))),relation_inverse(sK40))
| ~ in(sK25(relation_inverse(sK40),relation_dom(sK40)),relation_dom(sK40))
| ~ relation(relation_inverse(sK40))
| relation_rng(relation_inverse(sK40)) = relation_dom(sK40) ),
inference(instantiation,[status(thm)],[c_33549]) ).
cnf(c_39715,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_39714,c_38646,c_31293,c_23052,c_20362,c_19176,c_13852,c_12270,c_7566,c_6262,c_4848,c_4610,c_3699,c_236,c_237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU181+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 15:38:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 35.66/5.74 % SZS status Started for theBenchmark.p
% 35.66/5.74 % SZS status Theorem for theBenchmark.p
% 35.66/5.74
% 35.66/5.74 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 35.66/5.74
% 35.66/5.74 ------ iProver source info
% 35.66/5.74
% 35.66/5.74 git: date: 2023-05-31 18:12:56 +0000
% 35.66/5.74 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 35.66/5.74 git: non_committed_changes: false
% 35.66/5.74 git: last_make_outside_of_git: false
% 35.66/5.74
% 35.66/5.74 ------ Parsing...
% 35.66/5.74 ------ Clausification by vclausify_rel & Parsing by iProver...
% 35.66/5.74
% 35.66/5.74 ------ Preprocessing...
% 35.66/5.74
% 35.66/5.74 ------ Preprocessing...
% 35.66/5.74
% 35.66/5.74 ------ Preprocessing...
% 35.66/5.74 ------ Proving...
% 35.66/5.74 ------ Problem Properties
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74 clauses 214
% 35.66/5.74 conjectures 2
% 35.66/5.74 EPR 28
% 35.66/5.74 Horn 166
% 35.66/5.74 unary 38
% 35.66/5.74 binary 83
% 35.66/5.74 lits 516
% 35.66/5.74 lits eq 122
% 35.66/5.74 fd_pure 0
% 35.66/5.74 fd_pseudo 0
% 35.66/5.74 fd_cond 10
% 35.66/5.74 fd_pseudo_cond 47
% 35.66/5.74 AC symbols 0
% 35.66/5.74
% 35.66/5.74 ------ Input Options Time Limit: Unbounded
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74 ------
% 35.66/5.74 Current options:
% 35.66/5.74 ------
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74 ------ Proving...
% 35.66/5.74
% 35.66/5.74
% 35.66/5.74 % SZS status Theorem for theBenchmark.p
% 35.66/5.74
% 35.66/5.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.66/5.74
% 36.09/5.75
%------------------------------------------------------------------------------