TSTP Solution File: SET792+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET792+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 : Tue Apr 30 20:40:21 EDT 2024
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 8 unt; 0 def)
% Number of atoms : 342 ( 25 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 435 ( 160 ~; 162 |; 89 &)
% ( 14 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 230 ( 209 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> min(M,R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> min(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( ~ member(X,E)
| apply(R,X,X) )
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y )
& ! [X,Y,Z] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f14,plain,
! [R,E] :
( pd0_0(E,R)
<=> ( ! [X] :
( ~ member(X,E)
| apply(R,X,X) )
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y ) ) ),
introduced(predicate_definition,[f13]) ).
fof(f15,plain,
! [R,E] :
( order(R,E)
<=> ( pd0_0(E,R)
& ! [X,Y,Z] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) ),
inference(formula_renaming,[status(thm)],[f13,f14]) ).
fof(f16,plain,
! [R,E] :
( ( ~ order(R,E)
| ( pd0_0(E,R)
& ! [X,Y,Z] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ( order(R,E)
| ~ pd0_0(E,R)
| ? [X,Y,Z] :
( member(X,E)
& member(Y,E)
& member(Z,E)
& apply(R,X,Y)
& apply(R,Y,Z)
& ~ apply(R,X,Z) ) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [R,E] :
( ~ order(R,E)
| ( pd0_0(E,R)
& ! [X,Y,Z] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ! [R,E] :
( order(R,E)
| ~ pd0_0(E,R)
| ? [X,Y,Z] :
( member(X,E)
& member(Y,E)
& member(Z,E)
& apply(R,X,Y)
& apply(R,Y,Z)
& ~ apply(R,X,Z) ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [R,E] :
( ~ order(R,E)
| ( pd0_0(E,R)
& ! [X,Y,Z] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ member(Z,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ! [R,E] :
( order(R,E)
| ~ pd0_0(E,R)
| ( member(sk0_0(E,R),E)
& member(sk0_1(E,R),E)
& member(sk0_2(E,R),E)
& apply(R,sk0_0(E,R),sk0_1(E,R))
& apply(R,sk0_1(E,R),sk0_2(E,R))
& ~ apply(R,sk0_0(E,R),sk0_2(E,R)) ) ) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ order(X0,X1)
| pd0_0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f44,plain,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f45,plain,
! [R,E,M] :
( ( ~ lower_bound(M,R,E)
| ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) )
& ( lower_bound(M,R,E)
| ? [X] :
( member(X,E)
& ~ apply(R,M,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
( ! [R,E,M] :
( ~ lower_bound(M,R,E)
| ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) )
& ! [R,E,M] :
( lower_bound(M,R,E)
| ? [X] :
( member(X,E)
& ~ apply(R,M,X) ) ) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ! [R,E,M] :
( ~ lower_bound(M,R,E)
| ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) )
& ! [R,E,M] :
( lower_bound(M,R,E)
| ( member(sk0_6(M,E,R),E)
& ~ apply(R,M,sk0_6(M,E,R)) ) ) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ lower_bound(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| member(sk0_6(X0,X2,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| ~ apply(X1,X0,sk0_6(X0,X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f59,plain,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f60,plain,
! [R,E,M] :
( ( ~ least(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ) )
& ( least(M,R,E)
| ~ member(M,E)
| ? [X] :
( member(X,E)
& ~ apply(R,M,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
( ! [R,E,M] :
( ~ least(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ) )
& ! [R,E,M] :
( least(M,R,E)
| ~ member(M,E)
| ? [X] :
( member(X,E)
& ~ apply(R,M,X) ) ) ),
inference(miniscoping,[status(esa)],[f60]) ).
fof(f62,plain,
( ! [R,E,M] :
( ~ least(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ) )
& ! [R,E,M] :
( least(M,R,E)
| ~ member(M,E)
| ( member(sk0_8(M,E,R),E)
& ~ apply(R,M,sk0_8(M,E,R)) ) ) ),
inference(skolemization,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ least(X0,X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ least(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f62]) ).
fof(f76,plain,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ~ member(X,E)
| ~ apply(R,X,M)
| M = X ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f77,plain,
! [R,E,M] :
( ( ~ min(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| ~ apply(R,X,M)
| M = X ) ) )
& ( min(M,R,E)
| ~ member(M,E)
| ? [X] :
( member(X,E)
& apply(R,X,M)
& M != X ) ) ),
inference(NNF_transformation,[status(esa)],[f76]) ).
fof(f78,plain,
( ! [R,E,M] :
( ~ min(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| ~ apply(R,X,M)
| M = X ) ) )
& ! [R,E,M] :
( min(M,R,E)
| ~ member(M,E)
| ? [X] :
( member(X,E)
& apply(R,X,M)
& M != X ) ) ),
inference(miniscoping,[status(esa)],[f77]) ).
fof(f79,plain,
( ! [R,E,M] :
( ~ min(M,R,E)
| ( member(M,E)
& ! [X] :
( ~ member(X,E)
| ~ apply(R,X,M)
| M = X ) ) )
& ! [R,E,M] :
( min(M,R,E)
| ~ member(M,E)
| ( member(sk0_10(M,E,R),E)
& apply(R,sk0_10(M,E,R),M)
& M != sk0_10(M,E,R) ) ) ),
inference(skolemization,[status(esa)],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( min(X0,X1,X2)
| ~ member(X0,X2)
| member(sk0_10(X0,X2,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( min(X0,X1,X2)
| ~ member(X0,X2)
| apply(X1,sk0_10(X0,X2,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f84,plain,
! [X0,X1,X2] :
( min(X0,X1,X2)
| ~ member(X0,X2)
| X0 != sk0_10(X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f79]) ).
fof(f105,plain,
? [R,E,M] :
( order(R,E)
& least(M,R,E)
& ~ min(M,R,E) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f106,plain,
( order(sk0_13,sk0_14)
& least(sk0_15,sk0_13,sk0_14)
& ~ min(sk0_15,sk0_13,sk0_14) ),
inference(skolemization,[status(esa)],[f105]) ).
fof(f107,plain,
order(sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f108,plain,
least(sk0_15,sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f109,plain,
~ min(sk0_15,sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f106]) ).
fof(f110,plain,
! [R,E,X] :
( pd0_1(X,E,R)
<=> ( ~ member(X,E)
| apply(R,X,X) ) ),
introduced(predicate_definition,[f14]) ).
fof(f111,plain,
! [R,E] :
( pd0_0(E,R)
<=> ( ! [X] : pd0_1(X,E,R)
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y ) ) ),
inference(formula_renaming,[status(thm)],[f14,f110]) ).
fof(f112,plain,
! [R,E] :
( ( ~ pd0_0(E,R)
| ( ! [X] : pd0_1(X,E,R)
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y ) ) )
& ( pd0_0(E,R)
| ? [X] : ~ pd0_1(X,E,R)
| ? [X,Y] :
( member(X,E)
& member(Y,E)
& apply(R,X,Y)
& apply(R,Y,X)
& X != Y ) ) ),
inference(NNF_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
( ! [R,E] :
( ~ pd0_0(E,R)
| ( ! [X] : pd0_1(X,E,R)
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y ) ) )
& ! [R,E] :
( pd0_0(E,R)
| ? [X] : ~ pd0_1(X,E,R)
| ? [X,Y] :
( member(X,E)
& member(Y,E)
& apply(R,X,Y)
& apply(R,Y,X)
& X != Y ) ) ),
inference(miniscoping,[status(esa)],[f112]) ).
fof(f114,plain,
( ! [R,E] :
( ~ pd0_0(E,R)
| ( ! [X] : pd0_1(X,E,R)
& ! [X,Y] :
( ~ member(X,E)
| ~ member(Y,E)
| ~ apply(R,X,Y)
| ~ apply(R,Y,X)
| X = Y ) ) )
& ! [R,E] :
( pd0_0(E,R)
| ~ pd0_1(sk0_16(E,R),E,R)
| ( member(sk0_17(E,R),E)
& member(sk0_18(E,R),E)
& apply(R,sk0_17(E,R),sk0_18(E,R))
& apply(R,sk0_18(E,R),sk0_17(E,R))
& sk0_17(E,R) != sk0_18(E,R) ) ) ),
inference(skolemization,[status(esa)],[f113]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ~ pd0_0(X0,X1)
| ~ member(X2,X0)
| ~ member(X3,X0)
| ~ apply(X1,X2,X3)
| ~ apply(X1,X3,X2)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f127,plain,
member(sk0_15,sk0_14),
inference(resolution,[status(thm)],[f63,f108]) ).
fof(f320,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ apply(X3,X0,X2)
| ~ apply(X3,X2,X0)
| X0 = X2
| ~ order(X3,X1) ),
inference(resolution,[status(thm)],[f116,f19]) ).
fof(f321,plain,
! [X0,X1] :
( ~ member(X0,sk0_14)
| ~ member(X1,sk0_14)
| ~ apply(sk0_13,X0,X1)
| ~ apply(sk0_13,X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[f320,f107]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( lower_bound(X0,X1,X2)
| ~ least(X0,X1,X3)
| ~ member(sk0_6(X0,X2,X1),X3) ),
inference(resolution,[status(thm)],[f50,f64]) ).
fof(f357,plain,
( spl0_14
<=> member(sk0_15,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f359,plain,
( ~ member(sk0_15,sk0_14)
| spl0_14 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f366,plain,
( $false
| spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f127]) ).
fof(f367,plain,
spl0_14,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f405,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| ~ least(X0,X1,X2)
| lower_bound(X0,X1,X2) ),
inference(resolution,[status(thm)],[f353,f49]) ).
fof(f406,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| ~ least(X0,X1,X2) ),
inference(duplicate_literals_removal,[status(esa)],[f405]) ).
fof(f480,plain,
lower_bound(sk0_15,sk0_13,sk0_14),
inference(resolution,[status(thm)],[f406,f108]) ).
fof(f481,plain,
! [X0] :
( ~ member(X0,sk0_14)
| apply(sk0_13,sk0_15,X0) ),
inference(resolution,[status(thm)],[f480,f48]) ).
fof(f636,plain,
! [X0] :
( ~ member(X0,sk0_14)
| ~ apply(sk0_13,X0,sk0_15)
| ~ apply(sk0_13,sk0_15,X0)
| X0 = sk0_15 ),
inference(resolution,[status(thm)],[f321,f127]) ).
fof(f637,plain,
! [X0] :
( ~ member(X0,sk0_14)
| ~ apply(sk0_13,X0,sk0_15)
| X0 = sk0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f481]) ).
fof(f669,plain,
! [X0] :
( ~ member(sk0_10(sk0_15,X0,sk0_13),sk0_14)
| sk0_10(sk0_15,X0,sk0_13) = sk0_15
| min(sk0_15,sk0_13,X0)
| ~ member(sk0_15,X0) ),
inference(resolution,[status(thm)],[f637,f83]) ).
fof(f670,plain,
! [X0] :
( ~ member(sk0_10(sk0_15,X0,sk0_13),sk0_14)
| min(sk0_15,sk0_13,X0)
| ~ member(sk0_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f84]) ).
fof(f702,plain,
( spl0_45
<=> min(sk0_15,sk0_13,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f703,plain,
( min(sk0_15,sk0_13,sk0_14)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,plain,
( min(sk0_15,sk0_13,sk0_14)
| ~ member(sk0_15,sk0_14)
| min(sk0_15,sk0_13,sk0_14)
| ~ member(sk0_15,sk0_14) ),
inference(resolution,[status(thm)],[f670,f82]) ).
fof(f706,plain,
( spl0_45
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f705,f702,f357]) ).
fof(f707,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f109]) ).
fof(f708,plain,
~ spl0_45,
inference(contradiction_clause,[status(thm)],[f707]) ).
fof(f709,plain,
$false,
inference(sat_refutation,[status(thm)],[f367,f706,f708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET792+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n008.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 : Mon Apr 29 21:35:28 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.20/0.57 % Refutation found
% 0.20/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.60 % Elapsed time: 0.240509 seconds
% 0.20/0.60 % CPU time: 1.763295 seconds
% 0.20/0.60 % Total memory used: 66.474 MB
% 0.20/0.60 % Net memory used: 66.061 MB
%------------------------------------------------------------------------------