TSTP Solution File: SEU255+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU255+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 17:05:15 EDT 2023
% Result : Theorem 32.52s 5.20s
% Output : CNFRefutation 32.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 186 ( 24 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 219 ( 88 ~; 86 |; 30 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 3 sgn; 63 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,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(f85,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f152,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f204,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f230,conjecture,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f231,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[],[f230]) ).
fof(f291,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f393,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f449,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f152]) ).
fof(f450,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f449]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f204]) ).
fof(f533,plain,
? [X0,X1] :
( ~ antisymmetric(relation_restriction(X1,X0))
& antisymmetric(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f231]) ).
fof(f534,plain,
? [X0,X1] :
( ~ antisymmetric(relation_restriction(X1,X0))
& antisymmetric(X1)
& relation(X1) ),
inference(flattening,[],[f533]) ).
fof(f841,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f450]) ).
fof(f842,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f841]) ).
fof(f843,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X2,X1),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK83(X0) != sK84(X0)
& in(ordered_pair(sK84(X0),sK83(X0)),X0)
& in(ordered_pair(sK83(X0),sK84(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f844,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ( sK83(X0) != sK84(X0)
& in(ordered_pair(sK84(X0),sK83(X0)),X0)
& in(ordered_pair(sK83(X0),sK84(X0)),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83,sK84])],[f842,f843]) ).
fof(f901,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f494]) ).
fof(f902,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2) )
& ( ( in(X0,cartesian_product2(X1,X1))
& in(X0,X2) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f901]) ).
fof(f905,plain,
( ? [X0,X1] :
( ~ antisymmetric(relation_restriction(X1,X0))
& antisymmetric(X1)
& relation(X1) )
=> ( ~ antisymmetric(relation_restriction(sK106,sK105))
& antisymmetric(sK106)
& relation(sK106) ) ),
introduced(choice_axiom,[]) ).
fof(f906,plain,
( ~ antisymmetric(relation_restriction(sK106,sK105))
& antisymmetric(sK106)
& relation(sK106) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106])],[f534,f905]) ).
fof(f1185,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f1238,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f393]) ).
fof(f1329,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(ordered_pair(X4,X3),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f844]) ).
fof(f1330,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK83(X0),sK84(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f844]) ).
fof(f1331,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK84(X0),sK83(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f844]) ).
fof(f1332,plain,
! [X0] :
( antisymmetric(X0)
| sK83(X0) != sK84(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f844]) ).
fof(f1433,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f902]) ).
fof(f1467,plain,
relation(sK106),
inference(cnf_transformation,[],[f906]) ).
fof(f1468,plain,
antisymmetric(sK106),
inference(cnf_transformation,[],[f906]) ).
fof(f1469,plain,
~ antisymmetric(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f906]) ).
fof(f1577,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f291]) ).
fof(f1615,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1185,f1577]) ).
fof(f1727,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK84(X0),sK83(X0)),unordered_pair(sK84(X0),sK84(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1331,f1615]) ).
fof(f1728,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK83(X0),sK84(X0)),unordered_pair(sK83(X0),sK83(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1330,f1615]) ).
fof(f1729,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1329,f1615,f1615]) ).
cnf(c_313,plain,
( ~ relation(X0)
| relation(relation_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f1238]) ).
cnf(c_404,plain,
( sK83(X0) != sK84(X0)
| ~ relation(X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1332]) ).
cnf(c_405,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK84(X0),sK83(X0)),unordered_pair(sK84(X0),sK84(X0))),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1727]) ).
cnf(c_406,plain,
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK83(X0),sK84(X0)),unordered_pair(sK83(X0),sK83(X0))),X0)
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f1728]) ).
cnf(c_407,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ in(unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)),X2)
| ~ relation(X2)
| ~ antisymmetric(X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f1729]) ).
cnf(c_510,plain,
( ~ in(X0,relation_restriction(X1,X2))
| ~ relation(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f1433]) ).
cnf(c_542,negated_conjecture,
~ antisymmetric(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f1469]) ).
cnf(c_543,negated_conjecture,
antisymmetric(sK106),
inference(cnf_transformation,[],[f1468]) ).
cnf(c_544,negated_conjecture,
relation(sK106),
inference(cnf_transformation,[],[f1467]) ).
cnf(c_12712,plain,
( sK83(relation_restriction(sK106,sK105)) != sK84(relation_restriction(sK106,sK105))
| ~ relation(relation_restriction(sK106,sK105))
| antisymmetric(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_404]) ).
cnf(c_12713,plain,
( ~ relation(relation_restriction(sK106,sK105))
| in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| antisymmetric(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_405]) ).
cnf(c_12714,plain,
( ~ relation(relation_restriction(sK106,sK105))
| in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| antisymmetric(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_406]) ).
cnf(c_13651,plain,
( ~ relation(sK106)
| relation(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_313]) ).
cnf(c_14461,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_restriction(X2,X3))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2) ),
inference(instantiation,[status(thm)],[c_510]) ).
cnf(c_15115,plain,
( ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),X0)
| ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),X0)
| ~ relation(X0)
| ~ antisymmetric(X0)
| sK83(relation_restriction(sK106,sK105)) = sK84(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_407]) ).
cnf(c_16164,plain,
( ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| ~ relation(sK106)
| in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),sK106) ),
inference(instantiation,[status(thm)],[c_14461]) ).
cnf(c_16165,plain,
( ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),relation_restriction(sK106,sK105))
| ~ relation(sK106)
| in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),sK106) ),
inference(instantiation,[status(thm)],[c_14461]) ).
cnf(c_16168,plain,
( ~ in(unordered_pair(unordered_pair(sK83(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105))),unordered_pair(sK83(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105)))),sK106)
| ~ in(unordered_pair(unordered_pair(sK84(relation_restriction(sK106,sK105)),sK83(relation_restriction(sK106,sK105))),unordered_pair(sK84(relation_restriction(sK106,sK105)),sK84(relation_restriction(sK106,sK105)))),sK106)
| ~ relation(sK106)
| ~ antisymmetric(sK106)
| sK83(relation_restriction(sK106,sK105)) = sK84(relation_restriction(sK106,sK105)) ),
inference(instantiation,[status(thm)],[c_15115]) ).
cnf(c_16169,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16168,c_16165,c_16164,c_13651,c_12714,c_12713,c_12712,c_542,c_543,c_544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU255+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : run_iprover %s %d THM
% 0.08/0.29 % Computer : n004.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Aug 23 17:12:23 EDT 2023
% 0.08/0.29 % CPUTime :
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.52/5.20 % SZS status Started for theBenchmark.p
% 32.52/5.20 % SZS status Theorem for theBenchmark.p
% 32.52/5.20
% 32.52/5.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 32.52/5.20
% 32.52/5.20 ------ iProver source info
% 32.52/5.20
% 32.52/5.20 git: date: 2023-05-31 18:12:56 +0000
% 32.52/5.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 32.52/5.20 git: non_committed_changes: false
% 32.52/5.20 git: last_make_outside_of_git: false
% 32.52/5.20
% 32.52/5.20 ------ Parsing...
% 32.52/5.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 32.52/5.20
% 32.52/5.20 ------ Preprocessing...
% 32.52/5.20
% 32.52/5.20 ------ Preprocessing...
% 32.52/5.20
% 32.52/5.20 ------ Preprocessing...
% 32.52/5.20 ------ Proving...
% 32.52/5.20 ------ Problem Properties
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20 clauses 577
% 32.52/5.20 conjectures 3
% 32.52/5.20 EPR 96
% 32.52/5.20 Horn 450
% 32.52/5.20 unary 87
% 32.52/5.20 binary 147
% 32.52/5.20 lits 1674
% 32.52/5.20 lits eq 266
% 32.52/5.20 fd_pure 0
% 32.52/5.20 fd_pseudo 0
% 32.52/5.20 fd_cond 21
% 32.52/5.20 fd_pseudo_cond 99
% 32.52/5.20 AC symbols 0
% 32.52/5.20
% 32.52/5.20 ------ Input Options Time Limit: Unbounded
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20 ------
% 32.52/5.20 Current options:
% 32.52/5.20 ------
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20 ------ Proving...
% 32.52/5.20
% 32.52/5.20
% 32.52/5.20 % SZS status Theorem for theBenchmark.p
% 32.52/5.20
% 32.52/5.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.52/5.20
% 32.52/5.21
%------------------------------------------------------------------------------