TSTP Solution File: SET800+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:35:13 EDT 2023
% Result : Theorem 0.16s 0.36s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 165 ( 52 ~; 48 |; 50 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 119 (; 107 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,E)
& subset(X2,E)
& subset(X1,X2) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M1,X1,R,E)
& greatest_lower_bound(M2,X2,R,E) )
=> apply(R,M2,M1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,E)
& subset(X2,E)
& subset(X1,X2) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M1,X1,R,E)
& greatest_lower_bound(M2,X2,R,E) )
=> apply(R,M2,M1) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f109,plain,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( ~ member(X,E)
| apply(R,M,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f110,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)],[f109]) ).
fof(f111,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)],[f110]) ).
fof(f112,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_9(M,E,R),E)
& ~ apply(R,M,sk0_9(M,E,R)) ) ) ),
inference(skolemization,[status(esa)],[f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( ~ lower_bound(X0,X1,X2)
| ~ member(X3,X2)
| apply(X1,X0,X3) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f160,plain,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ~ member(M,E)
| ~ lower_bound(M,R,X)
| apply(R,M,A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f161,plain,
! [A,X,R,E] :
( ( ~ greatest_lower_bound(A,X,R,E)
| ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ~ member(M,E)
| ~ lower_bound(M,R,X)
| apply(R,M,A) ) ) )
& ( greatest_lower_bound(A,X,R,E)
| ~ member(A,X)
| ~ lower_bound(A,R,X)
| ? [M] :
( member(M,E)
& lower_bound(M,R,X)
& ~ apply(R,M,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f160]) ).
fof(f162,plain,
( ! [A,X,R,E] :
( ~ greatest_lower_bound(A,X,R,E)
| ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ~ member(M,E)
| ~ lower_bound(M,R,X)
| apply(R,M,A) ) ) )
& ! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
| ~ member(A,X)
| ~ lower_bound(A,R,X)
| ? [M] :
( member(M,E)
& lower_bound(M,R,X)
& ~ apply(R,M,A) ) ) ),
inference(miniscoping,[status(esa)],[f161]) ).
fof(f163,plain,
( ! [A,X,R,E] :
( ~ greatest_lower_bound(A,X,R,E)
| ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ~ member(M,E)
| ~ lower_bound(M,R,X)
| apply(R,M,A) ) ) )
& ! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
| ~ member(A,X)
| ~ lower_bound(A,R,X)
| ( member(sk0_15(E,R,X,A),E)
& lower_bound(sk0_15(E,R,X,A),R,X)
& ~ apply(R,sk0_15(E,R,X,A),A) ) ) ),
inference(skolemization,[status(esa)],[f162]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f163]) ).
fof(f170,plain,
? [R,E] :
( order(R,E)
& ? [X1,X2] :
( subset(X1,E)
& subset(X2,E)
& subset(X1,X2)
& ? [M1,M2] :
( greatest_lower_bound(M1,X1,R,E)
& greatest_lower_bound(M2,X2,R,E)
& ~ apply(R,M2,M1) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f23]) ).
fof(f171,plain,
( order(sk0_16,sk0_17)
& subset(sk0_18,sk0_17)
& subset(sk0_19,sk0_17)
& subset(sk0_18,sk0_19)
& greatest_lower_bound(sk0_20,sk0_18,sk0_16,sk0_17)
& greatest_lower_bound(sk0_21,sk0_19,sk0_16,sk0_17)
& ~ apply(sk0_16,sk0_21,sk0_20) ),
inference(skolemization,[status(esa)],[f170]) ).
fof(f175,plain,
subset(sk0_18,sk0_19),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f176,plain,
greatest_lower_bound(sk0_20,sk0_18,sk0_16,sk0_17),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f177,plain,
greatest_lower_bound(sk0_21,sk0_19,sk0_16,sk0_17),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f178,plain,
~ apply(sk0_16,sk0_21,sk0_20),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f198,plain,
member(sk0_20,sk0_18),
inference(resolution,[status(thm)],[f164,f176]) ).
fof(f199,plain,
lower_bound(sk0_21,sk0_16,sk0_19),
inference(resolution,[status(thm)],[f165,f177]) ).
fof(f202,plain,
! [X0] :
( ~ member(X0,sk0_18)
| member(X0,sk0_19) ),
inference(resolution,[status(thm)],[f28,f175]) ).
fof(f205,plain,
member(sk0_20,sk0_19),
inference(resolution,[status(thm)],[f202,f198]) ).
fof(f311,plain,
! [X0] :
( ~ member(X0,sk0_19)
| apply(sk0_16,sk0_21,X0) ),
inference(resolution,[status(thm)],[f113,f199]) ).
fof(f318,plain,
apply(sk0_16,sk0_21,sk0_20),
inference(resolution,[status(thm)],[f311,f205]) ).
fof(f319,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f318,f178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue May 30 10:15:40 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.5.1
% 0.16/0.36 % Refutation found
% 0.16/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.59 % Elapsed time: 0.041152 seconds
% 0.24/0.59 % CPU time: 0.084231 seconds
% 0.24/0.59 % Memory used: 9.554 MB
%------------------------------------------------------------------------------