TSTP Solution File: SET753+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET753+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : Fri May 3 03:01:26 EDT 2024
% Result : Theorem 45.97s 7.22s
% Output : CNFRefutation 45.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 3 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 184 ( 67 ~; 59 |; 45 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 135 ( 2 sgn 88 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X5,X0,X1,X2,X4] :
( ( subset(X4,X0)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> subset(image2(X5,intersection(X2,X4)),intersection(image2(X5,X2),image2(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa03) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1,X2,X4] :
( ( subset(X4,X0)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> subset(image2(X5,intersection(X2,X4)),intersection(image2(X5,X2),image2(X5,X4))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
inference(rectify,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f67,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4)))
& subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f68,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4)))
& subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f70,f71]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f74]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f99,f100]) ).
fof(f116,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4)))
& subset(X4,X1)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> ( ~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))
& subset(sK13,sK10)
& subset(sK12,sK10)
& maps(sK9,sK10,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))
& subset(sK13,sK10)
& subset(sK12,sK10)
& maps(sK9,sK10,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f68,f116]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f123,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f124,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f125,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f153,plain,
! [X2,X0,X1] :
( member(sK5(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f154,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( member(X2,image2(X0,X1))
| ~ apply(X0,X3,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f170,plain,
~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),
inference(cnf_transformation,[],[f117]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_55,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_56,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_84,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| member(X2,image2(X0,X3)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_85,plain,
( ~ member(X0,image2(X1,X2))
| apply(X1,sK5(X1,X2,X0),X0) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_86,plain,
( ~ member(X0,image2(X1,X2))
| member(sK5(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_98,negated_conjecture,
~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),
inference(cnf_transformation,[],[f170]) ).
cnf(c_174,plain,
( member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,intersection(sK12,sK13)))
| subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_296,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),intersection(image2(sK9,sK12),image2(sK9,sK13)))
| subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_564,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,intersection(sK12,sK13)))
| apply(sK9,sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))) ),
inference(instantiation,[status(thm)],[c_85]) ).
cnf(c_565,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,intersection(sK12,sK13)))
| member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),intersection(sK12,sK13)) ),
inference(instantiation,[status(thm)],[c_86]) ).
cnf(c_4283,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK12))
| ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK13))
| member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),intersection(image2(sK9,sK12),image2(sK9,sK13))) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_4541,plain,
( ~ apply(sK9,sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))))
| ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),X0)
| member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,X0)) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_8803,plain,
( ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),intersection(sK12,sK13))
| member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK13) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_8827,plain,
( ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),intersection(sK12,sK13))
| member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK12) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_14975,plain,
( ~ apply(sK9,sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))))
| ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK13)
| member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK13)) ),
inference(instantiation,[status(thm)],[c_4541]) ).
cnf(c_15051,plain,
( ~ apply(sK9,sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))))
| ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK12)
| member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK12)) ),
inference(instantiation,[status(thm)],[c_4541]) ).
cnf(c_15052,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_15051,c_14975,c_8827,c_8803,c_4283,c_564,c_565,c_296,c_174,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET753+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.06/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 20:10:51 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 45.97/7.22 % SZS status Started for theBenchmark.p
% 45.97/7.22 % SZS status Theorem for theBenchmark.p
% 45.97/7.22
% 45.97/7.22 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 45.97/7.22
% 45.97/7.22 ------ iProver source info
% 45.97/7.22
% 45.97/7.22 git: date: 2024-05-02 19:28:25 +0000
% 45.97/7.22 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 45.97/7.22 git: non_committed_changes: false
% 45.97/7.22
% 45.97/7.22 ------ Parsing...
% 45.97/7.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 45.97/7.22
% 45.97/7.22 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 45.97/7.22
% 45.97/7.22 ------ Preprocessing...
% 45.97/7.22
% 45.97/7.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 45.97/7.22 ------ Proving...
% 45.97/7.22 ------ Problem Properties
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22 clauses 53
% 45.97/7.22 conjectures 4
% 45.97/7.22 EPR 6
% 45.97/7.22 Horn 48
% 45.97/7.22 unary 8
% 45.97/7.22 binary 25
% 45.97/7.22 lits 132
% 45.97/7.22 lits eq 4
% 45.97/7.22 fd_pure 0
% 45.97/7.22 fd_pseudo 0
% 45.97/7.22 fd_cond 0
% 45.97/7.22 fd_pseudo_cond 3
% 45.97/7.22 AC symbols 0
% 45.97/7.22
% 45.97/7.22 ------ Input Options Time Limit: Unbounded
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22 ------
% 45.97/7.22 Current options:
% 45.97/7.22 ------
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22 ------ Proving...
% 45.97/7.22
% 45.97/7.22
% 45.97/7.22 % SZS status Theorem for theBenchmark.p
% 45.97/7.22
% 45.97/7.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.97/7.22
% 45.97/7.22
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