TSTP Solution File: SET143+4 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 15:06:47 EDT 2023
% Result : Theorem 39.85s 6.23s
% Output : CNFRefutation 39.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 68 ~; 61 |; 16 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 2 sgn; 61 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f12,conjecture,
! [X0,X1,X5] : equal_set(intersection(intersection(X0,X1),X5),intersection(X0,intersection(X1,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI08) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5] : equal_set(intersection(intersection(X0,X1),X5),intersection(X0,intersection(X1,X5))),
inference(negated_conjecture,[],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f23,plain,
~ ! [X0,X1,X2] : equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
? [X0,X1,X2] : ~ equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2))),
inference(ennf_transformation,[],[f23]) ).
fof(f30,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,[],[f25]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,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])],[f31,f32]) ).
fof(f35,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,[],[f15]) ).
fof(f36,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,[],[f35]) ).
fof(f52,plain,
( ? [X0,X1,X2] : ~ equal_set(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X1,X2)))
=> ~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f29,f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f81,plain,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(cnf_transformation,[],[f53]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_55,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_56,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_57,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_76,negated_conjecture,
~ equal_set(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),
inference(cnf_transformation,[],[f81]) ).
cnf(c_221,plain,
( member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_222,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5))
| subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_806,plain,
( ~ subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5)))
| ~ subset(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(resolution,[status(thm)],[c_76,c_52]) ).
cnf(c_2225,plain,
( member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2226,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5)))
| subset(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_8071,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_8072,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(intersection(sK3,sK4),sK5))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_12382,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_12383,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,intersection(sK4,sK5)))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_13760,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_13761,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK4,sK5))
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_13999,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_14000,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,sK4))
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_14088,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),X0)
| ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5)
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(X0,sK5)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_18321,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4))
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK5)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(intersection(sK3,sK4),sK5)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_18332,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5))
| ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK3)
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK3,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_22013,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),X0)
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(X0,sK4)) ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_22014,plain,
( ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK3)
| ~ member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),sK4)
| member(sK0(intersection(sK3,intersection(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_22013]) ).
cnf(c_24943,plain,
( ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK4)
| ~ member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),sK5)
| member(sK0(intersection(intersection(sK3,sK4),sK5),intersection(sK3,intersection(sK4,sK5))),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[c_14088]) ).
cnf(c_24944,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_24943,c_22014,c_18332,c_18321,c_13999,c_14000,c_13760,c_13761,c_12382,c_12383,c_8071,c_8072,c_2225,c_2226,c_806,c_221,c_222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 09:17:23 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 39.85/6.23 % SZS status Started for theBenchmark.p
% 39.85/6.23 % SZS status Theorem for theBenchmark.p
% 39.85/6.23
% 39.85/6.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 39.85/6.23
% 39.85/6.23 ------ iProver source info
% 39.85/6.23
% 39.85/6.23 git: date: 2023-05-31 18:12:56 +0000
% 39.85/6.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 39.85/6.23 git: non_committed_changes: false
% 39.85/6.23 git: last_make_outside_of_git: false
% 39.85/6.23
% 39.85/6.23 ------ Parsing...
% 39.85/6.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 39.85/6.23
% 39.85/6.23 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 39.85/6.23
% 39.85/6.23 ------ Preprocessing...
% 39.85/6.23
% 39.85/6.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 39.85/6.23 ------ Proving...
% 39.85/6.23 ------ Problem Properties
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23 clauses 28
% 39.85/6.23 conjectures 1
% 39.85/6.23 EPR 3
% 39.85/6.23 Horn 23
% 39.85/6.23 unary 5
% 39.85/6.23 binary 15
% 39.85/6.23 lits 59
% 39.85/6.23 lits eq 3
% 39.85/6.23 fd_pure 0
% 39.85/6.23 fd_pseudo 0
% 39.85/6.23 fd_cond 0
% 39.85/6.23 fd_pseudo_cond 2
% 39.85/6.23 AC symbols 0
% 39.85/6.23
% 39.85/6.23 ------ Input Options Time Limit: Unbounded
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23 ------
% 39.85/6.23 Current options:
% 39.85/6.23 ------
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23 ------ Proving...
% 39.85/6.23
% 39.85/6.23
% 39.85/6.23 % SZS status Theorem for theBenchmark.p
% 39.85/6.23
% 39.85/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 39.85/6.23
% 39.85/6.24
%------------------------------------------------------------------------------