TSTP Solution File: SEU239+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU239+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 03:05:10 EDT 2024
% Result : Theorem 32.32s 5.16s
% Output : CNFRefutation 32.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 8 unt; 0 def)
% Number of atoms : 191 ( 5 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 230 ( 92 ~; 91 |; 30 &)
% ( 6 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 55 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f48,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(f58,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f127,conjecture,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[],[f127]) ).
fof(f261,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f320,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f345,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f393,plain,
? [X0] :
( ( reflexive(X0)
<~> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f606,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f320]) ).
fof(f607,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f606]) ).
fof(f608,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
& in(sK21(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f609,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
& in(sK21(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f607,f608]) ).
fof(f723,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f345]) ).
fof(f726,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f393]) ).
fof(f727,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(flattening,[],[f726]) ).
fof(f728,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(rectify,[],[f727]) ).
fof(f729,plain,
( ? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) )
=> ( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK67)
& in(X1,relation_field(sK67)) )
| ~ reflexive(sK67) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67)) )
| reflexive(sK67) )
& relation(sK67) ) ),
introduced(choice_axiom,[]) ).
fof(f730,plain,
( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK67)
& in(X1,relation_field(sK67)) )
=> ( ~ in(ordered_pair(sK68,sK68),sK67)
& in(sK68,relation_field(sK67)) ) ),
introduced(choice_axiom,[]) ).
fof(f731,plain,
( ( ( ~ in(ordered_pair(sK68,sK68),sK67)
& in(sK68,relation_field(sK67)) )
| ~ reflexive(sK67) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67)) )
| reflexive(sK67) )
& relation(sK67) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f728,f730,f729]) ).
fof(f925,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f609]) ).
fof(f926,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK21(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f609]) ).
fof(f927,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f609]) ).
fof(f1030,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f1058,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f1059,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f723]) ).
fof(f1134,plain,
relation(sK67),
inference(cnf_transformation,[],[f731]) ).
fof(f1135,plain,
! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67))
| reflexive(sK67) ),
inference(cnf_transformation,[],[f731]) ).
fof(f1136,plain,
( in(sK68,relation_field(sK67))
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f731]) ).
fof(f1137,plain,
( ~ in(ordered_pair(sK68,sK68),sK67)
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f731]) ).
fof(f1367,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f261]) ).
fof(f1403,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1030,f1367]) ).
fof(f1434,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK21(X0,X1),sK21(X0,X1)),unordered_pair(sK21(X0,X1),sK21(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f927,f1403]) ).
fof(f1435,plain,
! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f925,f1403]) ).
fof(f1488,plain,
( ~ in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67)
| ~ reflexive(sK67) ),
inference(definition_unfolding,[],[f1137,f1403]) ).
fof(f1489,plain,
! [X2] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),sK67)
| ~ in(X2,relation_field(sK67))
| reflexive(sK67) ),
inference(definition_unfolding,[],[f1135,f1403]) ).
cnf(c_122,plain,
( ~ in(unordered_pair(unordered_pair(sK21(X0,X1),sK21(X0,X1)),unordered_pair(sK21(X0,X1),sK21(X0,X1))),X0)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f1434]) ).
cnf(c_123,plain,
( ~ relation(X0)
| in(sK21(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f926]) ).
cnf(c_124,plain,
( ~ in(X0,X1)
| ~ is_reflexive_in(X2,X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),X2) ),
inference(cnf_transformation,[],[f1435]) ).
cnf(c_254,plain,
( ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f1059]) ).
cnf(c_255,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f1058]) ).
cnf(c_330,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67)
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f1488]) ).
cnf(c_331,negated_conjecture,
( ~ reflexive(sK67)
| in(sK68,relation_field(sK67)) ),
inference(cnf_transformation,[],[f1136]) ).
cnf(c_332,negated_conjecture,
( ~ in(X0,relation_field(sK67))
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sK67)
| reflexive(sK67) ),
inference(cnf_transformation,[],[f1489]) ).
cnf(c_333,negated_conjecture,
relation(sK67),
inference(cnf_transformation,[],[f1134]) ).
cnf(c_10070,plain,
( ~ is_reflexive_in(X0,relation_field(sK67))
| ~ in(sK68,relation_field(sK67))
| ~ relation(X0)
| in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),X0) ),
inference(instantiation,[status(thm)],[c_124]) ).
cnf(c_10244,plain,
( ~ is_reflexive_in(sK67,relation_field(sK67))
| ~ relation(sK67)
| reflexive(sK67) ),
inference(instantiation,[status(thm)],[c_254]) ).
cnf(c_11529,plain,
( ~ relation(sK67)
| in(sK21(sK67,relation_field(sK67)),relation_field(sK67))
| is_reflexive_in(sK67,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_123]) ).
cnf(c_11530,plain,
( ~ in(unordered_pair(unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67))),unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67)))),sK67)
| ~ relation(sK67)
| is_reflexive_in(sK67,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_122]) ).
cnf(c_11531,plain,
( ~ relation(sK67)
| ~ reflexive(sK67)
| is_reflexive_in(sK67,relation_field(sK67)) ),
inference(instantiation,[status(thm)],[c_255]) ).
cnf(c_15134,plain,
( ~ in(sK21(sK67,relation_field(sK67)),relation_field(sK67))
| in(unordered_pair(unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67))),unordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67)))),sK67)
| reflexive(sK67) ),
inference(instantiation,[status(thm)],[c_332]) ).
cnf(c_15760,plain,
( ~ in(sK68,relation_field(sK67))
| ~ is_reflexive_in(sK67,relation_field(sK67))
| ~ relation(sK67)
| in(unordered_pair(unordered_pair(sK68,sK68),unordered_pair(sK68,sK68)),sK67) ),
inference(instantiation,[status(thm)],[c_10070]) ).
cnf(c_16771,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15760,c_15134,c_11531,c_11529,c_11530,c_10244,c_330,c_331,c_333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU239+2 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 17:57:21 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.32/5.16 % SZS status Started for theBenchmark.p
% 32.32/5.16 % SZS status Theorem for theBenchmark.p
% 32.32/5.16
% 32.32/5.16 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 32.32/5.16
% 32.32/5.16 ------ iProver source info
% 32.32/5.16
% 32.32/5.16 git: date: 2024-05-02 19:28:25 +0000
% 32.32/5.16 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 32.32/5.16 git: non_committed_changes: false
% 32.32/5.16
% 32.32/5.16 ------ Parsing...
% 32.32/5.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 32.32/5.16
% 32.32/5.16 ------ Preprocessing...
% 32.32/5.16
% 32.32/5.16 ------ Preprocessing...
% 32.32/5.16
% 32.32/5.16 ------ Preprocessing...
% 32.32/5.16 ------ Proving...
% 32.32/5.16 ------ Problem Properties
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16 clauses 487
% 32.32/5.16 conjectures 4
% 32.32/5.16 EPR 83
% 32.32/5.16 Horn 389
% 32.32/5.16 unary 85
% 32.32/5.16 binary 140
% 32.32/5.16 lits 1369
% 32.32/5.16 lits eq 243
% 32.32/5.16 fd_pure 0
% 32.32/5.16 fd_pseudo 0
% 32.32/5.16 fd_cond 17
% 32.32/5.16 fd_pseudo_cond 92
% 32.32/5.16 AC symbols 0
% 32.32/5.16
% 32.32/5.16 ------ Input Options Time Limit: Unbounded
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16 ------
% 32.32/5.16 Current options:
% 32.32/5.16 ------
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16 ------ Proving...
% 32.32/5.16
% 32.32/5.16
% 32.32/5.16 % SZS status Theorem for theBenchmark.p
% 32.32/5.16
% 32.32/5.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.32/5.16
% 32.32/5.17
%------------------------------------------------------------------------------