TSTP Solution File: SET798+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 20:40:22 EDT 2024
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 106 ( 35 ~; 33 |; 26 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 85 ( 76 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,E)
& subset(Y,E)
& subset(X,Y) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,E)
& subset(Y,E)
& subset(X,Y) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
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(f114,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| member(sk0_9(X0,X2,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f115,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| ~ apply(X1,X0,sk0_9(X0,X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f112]) ).
fof(f170,plain,
? [R,E] :
( order(R,E)
& ? [X,Y] :
( subset(X,E)
& subset(Y,E)
& subset(X,Y)
& ? [M] :
( lower_bound(M,R,Y)
& ~ lower_bound(M,R,X) ) ) ),
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)
& lower_bound(sk0_20,sk0_16,sk0_19)
& ~ lower_bound(sk0_20,sk0_16,sk0_18) ),
inference(skolemization,[status(esa)],[f170]) ).
fof(f175,plain,
subset(sk0_18,sk0_19),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f176,plain,
lower_bound(sk0_20,sk0_16,sk0_19),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f177,plain,
~ lower_bound(sk0_20,sk0_16,sk0_18),
inference(cnf_transformation,[status(esa)],[f171]) ).
fof(f199,plain,
! [X0] :
( ~ member(X0,sk0_19)
| apply(sk0_16,sk0_20,X0) ),
inference(resolution,[status(thm)],[f113,f176]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( lower_bound(X0,X1,X2)
| ~ subset(X2,X3)
| member(sk0_9(X0,X2,X1),X3) ),
inference(resolution,[status(thm)],[f114,f28]) ).
fof(f242,plain,
! [X0] :
( lower_bound(sk0_20,sk0_16,X0)
| ~ member(sk0_9(sk0_20,X0,sk0_16),sk0_19) ),
inference(resolution,[status(thm)],[f115,f199]) ).
fof(f268,plain,
! [X0] :
( lower_bound(sk0_20,sk0_16,X0)
| lower_bound(sk0_20,sk0_16,X0)
| ~ subset(X0,sk0_19) ),
inference(resolution,[status(thm)],[f242,f241]) ).
fof(f269,plain,
! [X0] :
( lower_bound(sk0_20,sk0_16,X0)
| ~ subset(X0,sk0_19) ),
inference(duplicate_literals_removal,[status(esa)],[f268]) ).
fof(f275,plain,
~ subset(sk0_18,sk0_19),
inference(resolution,[status(thm)],[f269,f177]) ).
fof(f276,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f275,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET798+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 29 21:53:05 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.6.0
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.32 % Elapsed time: 0.031501 seconds
% 0.14/0.32 % CPU time: 0.144805 seconds
% 0.14/0.32 % Total memory used: 27.894 MB
% 0.14/0.32 % Net memory used: 27.819 MB
%------------------------------------------------------------------------------