TSTP Solution File: SET797+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET797+4 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 : Mon Jun 24 14:36:02 EDT 2024
% Result : Theorem 6.98s 1.66s
% Output : CNFRefutation 6.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 180 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 199 ( 68 ~; 52 |; 57 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 136 ( 0 sgn 72 !; 29 ?)
% 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(f14,axiom,
! [X5,X3,X7] :
( upper_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X2,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_bound) ).
fof(f22,conjecture,
! [X5,X3] :
( order(X5,X3)
=> ! [X2,X4] :
( ( subset(X2,X4)
& subset(X4,X3)
& subset(X2,X3) )
=> ! [X7] :
( upper_bound(X7,X5,X4)
=> upper_bound(X7,X5,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV9) ).
fof(f23,negated_conjecture,
~ ! [X5,X3] :
( order(X5,X3)
=> ! [X2,X4] :
( ( subset(X2,X4)
& subset(X4,X3)
& subset(X2,X3) )
=> ! [X7] :
( upper_bound(X7,X5,X4)
=> upper_bound(X7,X5,X2) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f35,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ),
inference(rectify,[],[f14]) ).
fof(f43,plain,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4] :
( upper_bound(X4,X0,X3)
=> upper_bound(X4,X0,X2) ) ) ),
inference(rectify,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f49,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f50,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ upper_bound(X4,X0,X2)
& upper_bound(X4,X0,X3) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f51,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ upper_bound(X4,X0,X2)
& upper_bound(X4,X0,X3) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f52,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,[],[f45]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f55,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])],[f53,f54]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) )
=> ( ~ apply(X0,sK3(X0,X1,X2),X2)
& member(sK3(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ( ~ apply(X0,sK3(X0,X1,X2),X2)
& member(sK3(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f75,f76]) ).
fof(f78,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( ? [X4] :
( ~ upper_bound(X4,X0,X2)
& upper_bound(X4,X0,X3) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X3,X2] :
( ? [X4] :
( ~ upper_bound(X4,sK4,X2)
& upper_bound(X4,sK4,X3) )
& subset(X2,X3)
& subset(X3,sK5)
& subset(X2,sK5) )
& order(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
( ? [X3,X2] :
( ? [X4] :
( ~ upper_bound(X4,sK4,X2)
& upper_bound(X4,sK4,X3) )
& subset(X2,X3)
& subset(X3,sK5)
& subset(X2,sK5) )
=> ( ? [X4] :
( ~ upper_bound(X4,sK4,sK6)
& upper_bound(X4,sK4,sK7) )
& subset(sK6,sK7)
& subset(sK7,sK5)
& subset(sK6,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
( ? [X4] :
( ~ upper_bound(X4,sK4,sK6)
& upper_bound(X4,sK4,sK7) )
=> ( ~ upper_bound(sK8,sK4,sK6)
& upper_bound(sK8,sK4,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ~ upper_bound(sK8,sK4,sK6)
& upper_bound(sK8,sK4,sK7)
& subset(sK6,sK7)
& subset(sK7,sK5)
& subset(sK6,sK5)
& order(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f51,f80,f79,f78]) ).
fof(f82,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f112,plain,
! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| member(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X2,X0,X1] :
( upper_bound(X2,X0,X1)
| ~ apply(X0,sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f81]) ).
fof(f118,plain,
upper_bound(sK8,sK4,sK7),
inference(cnf_transformation,[],[f81]) ).
fof(f119,plain,
~ upper_bound(sK8,sK4,sK6),
inference(cnf_transformation,[],[f81]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_78,plain,
( ~ apply(X0,sK3(X0,X1,X2),X2)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_79,plain,
( member(sK3(X0,X1,X2),X1)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_80,plain,
( ~ upper_bound(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X3,X0) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_81,negated_conjecture,
~ upper_bound(sK8,sK4,sK6),
inference(cnf_transformation,[],[f119]) ).
cnf(c_82,negated_conjecture,
upper_bound(sK8,sK4,sK7),
inference(cnf_transformation,[],[f118]) ).
cnf(c_83,negated_conjecture,
subset(sK6,sK7),
inference(cnf_transformation,[],[f117]) ).
cnf(c_156,plain,
( ~ apply(X0,sK3(X0,X1,X2),X2)
| upper_bound(X2,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_78]) ).
cnf(c_166,plain,
( member(sK3(X0,X1,X2),X1)
| upper_bound(X2,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_79]) ).
cnf(c_587,plain,
( X0 != sK4
| X1 != sK6
| X2 != sK8
| member(sK3(X0,X1,X2),X1) ),
inference(resolution_lifted,[status(thm)],[c_166,c_81]) ).
cnf(c_588,plain,
member(sK3(sK4,sK6,sK8),sK6),
inference(unflattening,[status(thm)],[c_587]) ).
cnf(c_592,plain,
( X0 != sK4
| X1 != sK6
| X2 != sK8
| ~ apply(X0,sK3(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_156,c_81]) ).
cnf(c_593,plain,
~ apply(sK4,sK3(sK4,sK6,sK8),sK8),
inference(unflattening,[status(thm)],[c_592]) ).
cnf(c_2316,plain,
( ~ member(sK3(X0,X1,X2),X1)
| ~ subset(X1,X3)
| member(sK3(X0,X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_3616,plain,
( ~ member(sK3(X0,X1,X2),X3)
| ~ upper_bound(X2,X0,X3)
| apply(X0,sK3(X0,X1,X2),X2) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_18531,plain,
( ~ member(sK3(sK4,X0,sK8),sK7)
| ~ upper_bound(sK8,sK4,sK7)
| apply(sK4,sK3(sK4,X0,sK8),sK8) ),
inference(instantiation,[status(thm)],[c_3616]) ).
cnf(c_22115,plain,
( ~ member(sK3(sK4,sK6,sK8),sK6)
| ~ subset(sK6,X0)
| member(sK3(sK4,sK6,sK8),X0) ),
inference(instantiation,[status(thm)],[c_2316]) ).
cnf(c_24129,plain,
( ~ member(sK3(sK4,sK6,sK8),sK7)
| ~ upper_bound(sK8,sK4,sK7)
| apply(sK4,sK3(sK4,sK6,sK8),sK8) ),
inference(instantiation,[status(thm)],[c_18531]) ).
cnf(c_26503,plain,
( ~ member(sK3(sK4,sK6,sK8),sK6)
| ~ subset(sK6,sK7)
| member(sK3(sK4,sK6,sK8),sK7) ),
inference(instantiation,[status(thm)],[c_22115]) ).
cnf(c_26504,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_26503,c_24129,c_593,c_588,c_82,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET797+4 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n020.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 : Sun Jun 23 12:18:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 6.98/1.66 % SZS status Started for theBenchmark.p
% 6.98/1.66 % SZS status Theorem for theBenchmark.p
% 6.98/1.66
% 6.98/1.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.98/1.66
% 6.98/1.66 ------ iProver source info
% 6.98/1.66
% 6.98/1.66 git: date: 2024-06-12 09:56:46 +0000
% 6.98/1.66 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 6.98/1.66 git: non_committed_changes: false
% 6.98/1.66
% 6.98/1.66 ------ Parsing...
% 6.98/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.98/1.66
% 6.98/1.66 ------ Preprocessing... sup_sim: 0 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
% 6.98/1.66
% 6.98/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.98/1.66
% 6.98/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.98/1.66 ------ Proving...
% 6.98/1.66 ------ Problem Properties
% 6.98/1.66
% 6.98/1.66
% 6.98/1.66 clauses 37
% 6.98/1.66 conjectures 5
% 6.98/1.66 EPR 11
% 6.98/1.66 Horn 31
% 6.98/1.66 unary 9
% 6.98/1.66 binary 18
% 6.98/1.66 lits 80
% 6.98/1.66 lits eq 4
% 6.98/1.67 fd_pure 0
% 6.98/1.67 fd_pseudo 0
% 6.98/1.67 fd_cond 0
% 6.98/1.67 fd_pseudo_cond 3
% 6.98/1.67 AC symbols 0
% 6.98/1.67
% 6.98/1.67 ------ Schedule dynamic 5 is on
% 6.98/1.67
% 6.98/1.67 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.98/1.67
% 6.98/1.67
% 6.98/1.67 ------
% 6.98/1.67 Current options:
% 6.98/1.67 ------
% 6.98/1.67
% 6.98/1.67
% 6.98/1.67
% 6.98/1.67
% 6.98/1.67 ------ Proving...
% 6.98/1.67
% 6.98/1.67
% 6.98/1.67 % SZS status Theorem for theBenchmark.p
% 6.98/1.67
% 6.98/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.98/1.67
% 6.98/1.67
%------------------------------------------------------------------------------