TSTP Solution File: SEU009+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 17:03:23 EDT 2023
% Result : Theorem 3.14s 1.14s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 13 unt; 0 def)
% Number of atoms : 271 ( 40 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 354 ( 140 ~; 138 |; 58 &)
% ( 8 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 97 ( 2 sgn; 59 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f27,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(f29,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f31,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f58,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,[],[f27]) ).
fof(f59,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,[],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f66,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f65]) ).
fof(f91,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,[],[f59]) ).
fof(f92,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,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f94,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK9(X0,X1) != apply(X1,sK9(X0,X1))
& in(sK9(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK9(X0,X1) != apply(X1,sK9(X0,X1))
& in(sK9(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f95,f96]) ).
fof(f98,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f66]) ).
fof(f99,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
( ? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
& function(X2)
& relation(X2) )
=> ( ( ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12))
| ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) )
& ( ( in(apply(sK12,sK11),sK10)
& in(sK11,relation_dom(sK12)) )
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) )
& function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ( ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12))
| ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) )
& ( ( in(apply(sK12,sK11),sK10)
& in(sK11,relation_dom(sK12)) )
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) )
& function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f99,f100]) ).
fof(f116,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f117,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f140,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f142,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,[],[f92]) ).
fof(f144,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f149,plain,
relation(sK12),
inference(cnf_transformation,[],[f101]) ).
fof(f150,plain,
function(sK12),
inference(cnf_transformation,[],[f101]) ).
fof(f151,plain,
( in(sK11,relation_dom(sK12))
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f152,plain,
( in(apply(sK12,sK11),sK10)
| in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f153,plain,
( ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12))
| ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f144]) ).
cnf(c_63,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[],[f117]) ).
cnf(c_64,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[],[f116]) ).
cnf(c_87,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,[],[f142]) ).
cnf(c_88,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| in(apply(X1,X0),relation_dom(X2)) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_89,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_94,plain,
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_96,negated_conjecture,
( ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12)) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_97,negated_conjecture,
( in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| in(apply(sK12,sK11),sK10) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_98,negated_conjecture,
( in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| in(sK11,relation_dom(sK12)) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_99,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f150]) ).
cnf(c_100,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f149]) ).
cnf(c_135,plain,
relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_94,c_64,c_63,c_94]) ).
cnf(c_2190,plain,
( ~ function(identity_relation(sK10))
| ~ relation(identity_relation(sK10))
| ~ function(sK12)
| ~ relation(sK12)
| in(sK11,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_98,c_89]) ).
cnf(c_2192,plain,
in(sK11,relation_dom(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_2190,c_100,c_99,c_64,c_63]) ).
cnf(c_2207,plain,
( ~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10))))
| ~ in(apply(sK12,sK11),sK10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_2192]) ).
cnf(c_2225,plain,
( ~ function(identity_relation(sK10))
| ~ relation(identity_relation(sK10))
| ~ function(sK12)
| ~ relation(sK12)
| in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| in(apply(sK12,sK11),sK10) ),
inference(superposition,[status(thm)],[c_97,c_88]) ).
cnf(c_2227,plain,
( in(apply(sK12,sK11),relation_dom(identity_relation(sK10)))
| in(apply(sK12,sK11),sK10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2225,c_100,c_99,c_64,c_63]) ).
cnf(c_2251,plain,
in(apply(sK12,sK11),sK10),
inference(demodulation,[status(thm)],[c_2227,c_135]) ).
cnf(c_2256,plain,
~ in(sK11,relation_dom(relation_composition(sK12,identity_relation(sK10)))),
inference(forward_subsumption_resolution,[status(thm)],[c_2207,c_2251]) ).
cnf(c_2290,plain,
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(identity_relation(X2))
| ~ relation(identity_relation(X2))
| ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) ),
inference(superposition,[status(thm)],[c_135,c_87]) ).
cnf(c_2291,plain,
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2290,c_64,c_63]) ).
cnf(c_2540,plain,
( ~ in(apply(sK12,sK11),sK10)
| ~ in(sK11,relation_dom(sK12))
| ~ function(sK12)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_2291,c_2256]) ).
cnf(c_2543,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2540,c_100,c_99,c_2192,c_2251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 14:18:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.14/1.14 % SZS status Started for theBenchmark.p
% 3.14/1.14 % SZS status Theorem for theBenchmark.p
% 3.14/1.14
% 3.14/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.14/1.14
% 3.14/1.14 ------ iProver source info
% 3.14/1.14
% 3.14/1.14 git: date: 2023-05-31 18:12:56 +0000
% 3.14/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.14/1.14 git: non_committed_changes: false
% 3.14/1.14 git: last_make_outside_of_git: false
% 3.14/1.14
% 3.14/1.14 ------ Parsing...
% 3.14/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.14/1.14
% 3.14/1.14 ------ Preprocessing... sup_sim: 0 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
% 3.14/1.14
% 3.14/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.14/1.14
% 3.14/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.14/1.14 ------ Proving...
% 3.14/1.14 ------ Problem Properties
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14 clauses 51
% 3.14/1.14 conjectures 5
% 3.14/1.14 EPR 21
% 3.14/1.14 Horn 46
% 3.14/1.14 unary 21
% 3.14/1.14 binary 13
% 3.14/1.14 lits 112
% 3.14/1.14 lits eq 7
% 3.14/1.14 fd_pure 0
% 3.14/1.14 fd_pseudo 0
% 3.14/1.14 fd_cond 1
% 3.14/1.14 fd_pseudo_cond 1
% 3.14/1.14 AC symbols 0
% 3.14/1.14
% 3.14/1.14 ------ Schedule dynamic 5 is on
% 3.14/1.14
% 3.14/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14 ------
% 3.14/1.14 Current options:
% 3.14/1.14 ------
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14 ------ Proving...
% 3.14/1.14
% 3.14/1.14
% 3.14/1.14 % SZS status Theorem for theBenchmark.p
% 3.14/1.14
% 3.14/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 3.14/1.14
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