TSTP Solution File: SEU215+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 17:04:47 EDT 2023
% Result : Theorem 3.61s 1.19s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 13 unt; 0 def)
% Number of atoms : 285 ( 47 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 368 ( 142 ~; 139 |; 60 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn; 69 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1,X2] :
( ( ~ in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> empty_set = X2 ) )
& ( in(X1,relation_dom(X0))
=> ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f18,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f36,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( apply(X0,X1) = X2
<=> empty_set = X2 )
| in(X1,relation_dom(X0)) )
& ( ( apply(X0,X1) = X2
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f50,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f54,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f53]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f66,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f65]) ).
fof(f72,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( apply(X0,X1) = X2
| empty_set != X2 )
& ( empty_set = X2
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) )
& ( ( ( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2)) )
& ( ( in(apply(X2,X0),relation_dom(X1))
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
( ? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
& in(X0,relation_dom(X1))
& function(X2)
& relation(X2) )
& function(X1)
& relation(X1) )
=> ( ? [X2] :
( apply(relation_composition(sK8,X2),sK7) != apply(X2,apply(sK8,sK7))
& in(sK7,relation_dom(sK8))
& function(X2)
& relation(X2) )
& function(sK8)
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X2] :
( apply(relation_composition(sK8,X2),sK7) != apply(X2,apply(sK8,sK7))
& in(sK7,relation_dom(sK8))
& function(X2)
& relation(X2) )
=> ( apply(relation_composition(sK8,sK9),sK7) != apply(sK9,apply(sK8,sK7))
& in(sK7,relation_dom(sK8))
& function(sK9)
& relation(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
( apply(relation_composition(sK8,sK9),sK7) != apply(sK9,apply(sK8,sK7))
& in(sK7,relation_dom(sK8))
& function(sK9)
& relation(sK9)
& function(sK8)
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f66,f90,f89]) ).
fof(f98,plain,
! [X2,X0,X1] :
( empty_set = X2
| apply(X0,X1) != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f108,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f132,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f133,plain,
! [X2,X0,X1] :
( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f134,plain,
relation(sK8),
inference(cnf_transformation,[],[f91]) ).
fof(f135,plain,
function(sK8),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
relation(sK9),
inference(cnf_transformation,[],[f91]) ).
fof(f137,plain,
function(sK9),
inference(cnf_transformation,[],[f91]) ).
fof(f138,plain,
in(sK7,relation_dom(sK8)),
inference(cnf_transformation,[],[f91]) ).
fof(f139,plain,
apply(relation_composition(sK8,sK9),sK7) != apply(sK9,apply(sK8,sK7)),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f98]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) = empty_set
| in(X1,relation_dom(X0)) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_57,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_63,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_86,plain,
( ~ in(apply(X0,X1),relation_dom(X2))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X2)
| in(X1,relation_dom(relation_composition(X0,X2))) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_89,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_90,negated_conjecture,
apply(relation_composition(sK8,sK9),sK7) != apply(sK9,apply(sK8,sK7)),
inference(cnf_transformation,[],[f139]) ).
cnf(c_91,negated_conjecture,
in(sK7,relation_dom(sK8)),
inference(cnf_transformation,[],[f138]) ).
cnf(c_92,negated_conjecture,
function(sK9),
inference(cnf_transformation,[],[f137]) ).
cnf(c_93,negated_conjecture,
relation(sK9),
inference(cnf_transformation,[],[f136]) ).
cnf(c_94,negated_conjecture,
function(sK8),
inference(cnf_transformation,[],[f135]) ).
cnf(c_95,negated_conjecture,
relation(sK8),
inference(cnf_transformation,[],[f134]) ).
cnf(c_897,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_1887,plain,
( apply(relation_composition(sK8,sK9),sK7) != X0
| apply(sK9,apply(sK8,sK7)) != X0
| apply(relation_composition(sK8,sK9),sK7) = apply(sK9,apply(sK8,sK7)) ),
inference(instantiation,[status(thm)],[c_897]) ).
cnf(c_1888,plain,
( apply(relation_composition(sK8,sK9),sK7) != empty_set
| apply(sK9,apply(sK8,sK7)) != empty_set
| apply(relation_composition(sK8,sK9),sK7) = apply(sK9,apply(sK8,sK7)) ),
inference(instantiation,[status(thm)],[c_1887]) ).
cnf(c_1962,plain,
( ~ in(apply(sK8,sK7),relation_dom(X0))
| ~ in(sK7,relation_dom(sK8))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK8)
| ~ relation(sK8)
| in(sK7,relation_dom(relation_composition(sK8,X0))) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_2477,plain,
( ~ function(sK8)
| ~ function(sK9)
| ~ relation(sK8)
| ~ relation(sK9)
| function(relation_composition(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2500,plain,
( ~ function(relation_composition(sK8,sK9))
| ~ relation(relation_composition(sK8,sK9))
| apply(relation_composition(sK8,sK9),sK7) = empty_set
| in(sK7,relation_dom(relation_composition(sK8,sK9))) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_3313,plain,
( ~ relation(sK8)
| ~ relation(sK9)
| relation(relation_composition(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_3433,plain,
( ~ function(sK9)
| ~ relation(sK9)
| apply(sK9,apply(sK8,sK7)) = empty_set
| in(apply(sK8,sK7),relation_dom(sK9)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_4805,plain,
( ~ in(sK7,relation_dom(relation_composition(sK8,sK9)))
| ~ function(sK8)
| ~ function(sK9)
| ~ relation(sK8)
| ~ relation(sK9)
| apply(relation_composition(sK8,sK9),sK7) = apply(sK9,apply(sK8,sK7)) ),
inference(instantiation,[status(thm)],[c_89]) ).
cnf(c_7217,plain,
( ~ in(apply(sK8,sK7),relation_dom(sK9))
| ~ in(sK7,relation_dom(sK8))
| ~ function(sK8)
| ~ function(sK9)
| ~ relation(sK8)
| ~ relation(sK9)
| in(sK7,relation_dom(relation_composition(sK8,sK9))) ),
inference(instantiation,[status(thm)],[c_1962]) ).
cnf(c_7218,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7217,c_4805,c_3433,c_3313,c_2500,c_2477,c_1888,c_90,c_91,c_92,c_93,c_94,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU215+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.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 22:06:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.61/1.19 % SZS status Started for theBenchmark.p
% 3.61/1.19 % SZS status Theorem for theBenchmark.p
% 3.61/1.19
% 3.61/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.61/1.19
% 3.61/1.19 ------ iProver source info
% 3.61/1.19
% 3.61/1.19 git: date: 2023-05-31 18:12:56 +0000
% 3.61/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.61/1.19 git: non_committed_changes: false
% 3.61/1.19 git: last_make_outside_of_git: false
% 3.61/1.19
% 3.61/1.19 ------ Parsing...
% 3.61/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.61/1.19
% 3.61/1.19 ------ Preprocessing... sup_sim: 2 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
% 3.61/1.19
% 3.61/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.61/1.19
% 3.61/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.61/1.19 ------ Proving...
% 3.61/1.19 ------ Problem Properties
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 clauses 43
% 3.61/1.19 conjectures 6
% 3.61/1.19 EPR 21
% 3.61/1.19 Horn 41
% 3.61/1.19 unary 20
% 3.61/1.19 binary 8
% 3.61/1.19 lits 100
% 3.61/1.19 lits eq 7
% 3.61/1.19 fd_pure 0
% 3.61/1.19 fd_pseudo 0
% 3.61/1.19 fd_cond 1
% 3.61/1.19 fd_pseudo_cond 2
% 3.61/1.19 AC symbols 0
% 3.61/1.19
% 3.61/1.19 ------ Schedule dynamic 5 is on
% 3.61/1.19
% 3.61/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 ------
% 3.61/1.19 Current options:
% 3.61/1.19 ------
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 ------ Proving...
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 % SZS status Theorem for theBenchmark.p
% 3.61/1.19
% 3.61/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.61/1.19
% 3.61/1.19
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