TSTP Solution File: SEU215+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 0.80s 1.16s
% Output : CNFRefutation 0.80s
% 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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f7,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f31,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/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f33,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/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f34,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,[],[f33]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f56,plain,
! [X0,X1] :
( ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f64,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,[],[f31]) ).
fof(f65,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,[],[f64]) ).
fof(f66,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,[],[f32]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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,[],[f34]) ).
fof(f69,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,[],[f68]) ).
fof(f79,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,[],[f50]) ).
fof(f98,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,[],[f65]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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(sK10,X2),sK9) != apply(X2,apply(sK10,sK9))
& in(sK9,relation_dom(sK10))
& function(X2)
& relation(X2) )
& function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X2] :
( apply(relation_composition(sK10,X2),sK9) != apply(X2,apply(sK10,sK9))
& in(sK9,relation_dom(sK10))
& function(X2)
& relation(X2) )
=> ( apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9))
& in(sK9,relation_dom(sK10))
& function(sK11)
& relation(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9))
& in(sK9,relation_dom(sK10))
& function(sK11)
& relation(sK11)
& function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f69,f101,f100]) ).
fof(f109,plain,
! [X2,X0,X1] :
( empty_set = X2
| apply(X0,X1) != X2
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f112,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f119,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f149,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,[],[f99]) ).
fof(f150,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,[],[f67]) ).
fof(f151,plain,
relation(sK10),
inference(cnf_transformation,[],[f102]) ).
fof(f152,plain,
function(sK10),
inference(cnf_transformation,[],[f102]) ).
fof(f153,plain,
relation(sK11),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
function(sK11),
inference(cnf_transformation,[],[f102]) ).
fof(f155,plain,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
inference(cnf_transformation,[],[f102]) ).
fof(f168,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f109]) ).
cnf(c_54,plain,
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) = empty_set
| in(X1,relation_dom(X0)) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_57,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_63,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_92,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,[],[f149]) ).
cnf(c_95,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,[],[f150]) ).
cnf(c_96,negated_conjecture,
apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
inference(cnf_transformation,[],[f156]) ).
cnf(c_97,negated_conjecture,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f155]) ).
cnf(c_98,negated_conjecture,
function(sK11),
inference(cnf_transformation,[],[f154]) ).
cnf(c_99,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f153]) ).
cnf(c_100,negated_conjecture,
function(sK10),
inference(cnf_transformation,[],[f152]) ).
cnf(c_101,negated_conjecture,
relation(sK10),
inference(cnf_transformation,[],[f151]) ).
cnf(c_1025,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_2207,plain,
( apply(relation_composition(sK10,sK11),sK9) != X0
| apply(sK11,apply(sK10,sK9)) != X0
| apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_1025]) ).
cnf(c_2208,plain,
( apply(relation_composition(sK10,sK11),sK9) != empty_set
| apply(sK11,apply(sK10,sK9)) != empty_set
| apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_2207]) ).
cnf(c_2274,plain,
( ~ in(apply(sK10,sK9),relation_dom(X0))
| ~ in(sK9,relation_dom(sK10))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK10)
| ~ relation(sK10)
| in(sK9,relation_dom(relation_composition(sK10,X0))) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_2915,plain,
( ~ function(sK10)
| ~ function(sK11)
| ~ relation(sK10)
| ~ relation(sK11)
| function(relation_composition(sK10,sK11)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_2941,plain,
( ~ function(relation_composition(sK10,sK11))
| ~ relation(relation_composition(sK10,sK11))
| apply(relation_composition(sK10,sK11),sK9) = empty_set
| in(sK9,relation_dom(relation_composition(sK10,sK11))) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_4735,plain,
( ~ relation(sK10)
| ~ relation(sK11)
| relation(relation_composition(sK10,sK11)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_4752,plain,
( ~ function(sK11)
| ~ relation(sK11)
| apply(sK11,apply(sK10,sK9)) = empty_set
| in(apply(sK10,sK9),relation_dom(sK11)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_5401,plain,
( ~ in(sK9,relation_dom(relation_composition(sK10,sK11)))
| ~ function(sK10)
| ~ function(sK11)
| ~ relation(sK10)
| ~ relation(sK11)
| apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_9866,plain,
( ~ in(apply(sK10,sK9),relation_dom(sK11))
| ~ in(sK9,relation_dom(sK10))
| ~ function(sK10)
| ~ function(sK11)
| ~ relation(sK10)
| ~ relation(sK11)
| in(sK9,relation_dom(relation_composition(sK10,sK11))) ),
inference(instantiation,[status(thm)],[c_2274]) ).
cnf(c_9867,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9866,c_5401,c_4752,c_4735,c_2941,c_2915,c_2208,c_96,c_97,c_98,c_99,c_100,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n023.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 16:21:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.80/1.16 % SZS status Started for theBenchmark.p
% 0.80/1.16 % SZS status Theorem for theBenchmark.p
% 0.80/1.16
% 0.80/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.16
% 0.80/1.16 ------ iProver source info
% 0.80/1.16
% 0.80/1.16 git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.16 git: non_committed_changes: false
% 0.80/1.16 git: last_make_outside_of_git: false
% 0.80/1.16
% 0.80/1.16 ------ Parsing...
% 0.80/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.80/1.16
% 0.80/1.16 ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.80/1.16
% 0.80/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.80/1.16
% 0.80/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.80/1.16 ------ Proving...
% 0.80/1.16 ------ Problem Properties
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 clauses 53
% 0.80/1.16 conjectures 6
% 0.80/1.16 EPR 23
% 0.80/1.16 Horn 50
% 0.80/1.16 unary 25
% 0.80/1.16 binary 10
% 0.80/1.16 lits 118
% 0.80/1.16 lits eq 7
% 0.80/1.16 fd_pure 0
% 0.80/1.16 fd_pseudo 0
% 0.80/1.16 fd_cond 1
% 0.80/1.16 fd_pseudo_cond 2
% 0.80/1.16 AC symbols 0
% 0.80/1.16
% 0.80/1.16 ------ Schedule dynamic 5 is on
% 0.80/1.16
% 0.80/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 ------
% 0.80/1.16 Current options:
% 0.80/1.16 ------
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 ------ Proving...
% 0.80/1.16
% 0.80/1.16
% 0.80/1.16 % SZS status Theorem for theBenchmark.p
% 0.80/1.16
% 0.80/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.16
% 0.80/1.17
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