TSTP Solution File: SET766+4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 20:40:18 EDT 2024
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 248 ( 88 ~; 84 |; 62 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 134 ( 119 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X] :
( member(X,A)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,A)
& member(Y,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X,Y,Z] :
( ( member(X,A)
& member(Y,A)
& member(Z,A) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( member(X,E)
& apply(R,A,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [E,R,A] :
( ( equivalence(R,E)
& member(A,E) )
=> member(A,equivalence_class(A,E,R)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [E,R,A] :
( ( equivalence(R,E)
& member(A,E) )
=> member(A,equivalence_class(A,E,R)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f93,plain,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X] :
( ~ member(X,A)
| apply(R,X,X) )
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) )
& ! [X,Y,Z] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ member(Z,A)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f94,plain,
! [A,R] :
( pd0_1(R,A)
<=> ( ! [X] :
( ~ member(X,A)
| apply(R,X,X) )
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) ) ) ),
introduced(predicate_definition,[f93]) ).
fof(f95,plain,
! [A,R] :
( equivalence(R,A)
<=> ( pd0_1(R,A)
& ! [X,Y,Z] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ member(Z,A)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) ),
inference(formula_renaming,[status(thm)],[f93,f94]) ).
fof(f96,plain,
! [A,R] :
( ( ~ equivalence(R,A)
| ( pd0_1(R,A)
& ! [X,Y,Z] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ member(Z,A)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ( equivalence(R,A)
| ~ pd0_1(R,A)
| ? [X,Y,Z] :
( member(X,A)
& member(Y,A)
& member(Z,A)
& apply(R,X,Y)
& apply(R,Y,Z)
& ~ apply(R,X,Z) ) ) ),
inference(NNF_transformation,[status(esa)],[f95]) ).
fof(f97,plain,
( ! [A,R] :
( ~ equivalence(R,A)
| ( pd0_1(R,A)
& ! [X,Y,Z] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ member(Z,A)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ! [A,R] :
( equivalence(R,A)
| ~ pd0_1(R,A)
| ? [X,Y,Z] :
( member(X,A)
& member(Y,A)
& member(Z,A)
& apply(R,X,Y)
& apply(R,Y,Z)
& ~ apply(R,X,Z) ) ) ),
inference(miniscoping,[status(esa)],[f96]) ).
fof(f98,plain,
( ! [A,R] :
( ~ equivalence(R,A)
| ( pd0_1(R,A)
& ! [X,Y,Z] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ member(Z,A)
| ~ apply(R,X,Y)
| ~ apply(R,Y,Z)
| apply(R,X,Z) ) ) )
& ! [A,R] :
( equivalence(R,A)
| ~ pd0_1(R,A)
| ( member(sk0_7(R,A),A)
& member(sk0_8(R,A),A)
& member(sk0_9(R,A),A)
& apply(R,sk0_7(R,A),sk0_8(R,A))
& apply(R,sk0_8(R,A),sk0_9(R,A))
& ~ apply(R,sk0_7(R,A),sk0_9(R,A)) ) ) ),
inference(skolemization,[status(esa)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ equivalence(X0,X1)
| pd0_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f107,plain,
! [R,E,A,X] :
( ( ~ member(X,equivalence_class(A,E,R))
| ( member(X,E)
& apply(R,A,X) ) )
& ( member(X,equivalence_class(A,E,R))
| ~ member(X,E)
| ~ apply(R,A,X) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f108,plain,
( ! [R,E,A,X] :
( ~ member(X,equivalence_class(A,E,R))
| ( member(X,E)
& apply(R,A,X) ) )
& ! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
| ~ member(X,E)
| ~ apply(R,A,X) ) ),
inference(miniscoping,[status(esa)],[f107]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( member(X0,equivalence_class(X1,X2,X3))
| ~ member(X0,X2)
| ~ apply(X3,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f126,plain,
? [E,R,A] :
( equivalence(R,E)
& member(A,E)
& ~ member(A,equivalence_class(A,E,R)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f127,plain,
( equivalence(sk0_15,sk0_14)
& member(sk0_16,sk0_14)
& ~ member(sk0_16,equivalence_class(sk0_16,sk0_14,sk0_15)) ),
inference(skolemization,[status(esa)],[f126]) ).
fof(f128,plain,
equivalence(sk0_15,sk0_14),
inference(cnf_transformation,[status(esa)],[f127]) ).
fof(f129,plain,
member(sk0_16,sk0_14),
inference(cnf_transformation,[status(esa)],[f127]) ).
fof(f130,plain,
~ member(sk0_16,equivalence_class(sk0_16,sk0_14,sk0_15)),
inference(cnf_transformation,[status(esa)],[f127]) ).
fof(f141,plain,
! [A,R,X] :
( pd0_3(X,R,A)
<=> ( ~ member(X,A)
| apply(R,X,X) ) ),
introduced(predicate_definition,[f94]) ).
fof(f142,plain,
! [A,R] :
( pd0_1(R,A)
<=> ( ! [X] : pd0_3(X,R,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) ) ) ),
inference(formula_renaming,[status(thm)],[f94,f141]) ).
fof(f143,plain,
! [A,R] :
( ( ~ pd0_1(R,A)
| ( ! [X] : pd0_3(X,R,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) ) ) )
& ( pd0_1(R,A)
| ? [X] : ~ pd0_3(X,R,A)
| ? [X,Y] :
( member(X,A)
& member(Y,A)
& apply(R,X,Y)
& ~ apply(R,Y,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f142]) ).
fof(f144,plain,
( ! [A,R] :
( ~ pd0_1(R,A)
| ( ! [X] : pd0_3(X,R,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) ) ) )
& ! [A,R] :
( pd0_1(R,A)
| ? [X] : ~ pd0_3(X,R,A)
| ? [X,Y] :
( member(X,A)
& member(Y,A)
& apply(R,X,Y)
& ~ apply(R,Y,X) ) ) ),
inference(miniscoping,[status(esa)],[f143]) ).
fof(f145,plain,
( ! [A,R] :
( ~ pd0_1(R,A)
| ( ! [X] : pd0_3(X,R,A)
& ! [X,Y] :
( ~ member(X,A)
| ~ member(Y,A)
| ~ apply(R,X,Y)
| apply(R,Y,X) ) ) )
& ! [A,R] :
( pd0_1(R,A)
| ~ pd0_3(sk0_20(R,A),R,A)
| ( member(sk0_21(R,A),A)
& member(sk0_22(R,A),A)
& apply(R,sk0_21(R,A),sk0_22(R,A))
& ~ apply(R,sk0_22(R,A),sk0_21(R,A)) ) ) ),
inference(skolemization,[status(esa)],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1)
| pd0_3(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f157,plain,
! [A,R,X] :
( ( ~ pd0_3(X,R,A)
| ~ member(X,A)
| apply(R,X,X) )
& ( pd0_3(X,R,A)
| ( member(X,A)
& ~ apply(R,X,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f141]) ).
fof(f158,plain,
( ! [A,R,X] :
( ~ pd0_3(X,R,A)
| ~ member(X,A)
| apply(R,X,X) )
& ! [A,R,X] :
( pd0_3(X,R,A)
| ( member(X,A)
& ~ apply(R,X,X) ) ) ),
inference(miniscoping,[status(esa)],[f157]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ~ pd0_3(X0,X1,X2)
| ~ member(X0,X2)
| apply(X1,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f158]) ).
fof(f165,plain,
pd0_1(sk0_15,sk0_14),
inference(resolution,[status(thm)],[f99,f128]) ).
fof(f167,plain,
! [X0,X1] :
( member(sk0_16,equivalence_class(X0,sk0_14,X1))
| ~ apply(X1,X0,sk0_16) ),
inference(resolution,[status(thm)],[f111,f129]) ).
fof(f168,plain,
! [X0] : pd0_3(X0,sk0_15,sk0_14),
inference(resolution,[status(thm)],[f146,f165]) ).
fof(f171,plain,
! [X0] :
( ~ member(X0,sk0_14)
| apply(sk0_15,X0,X0) ),
inference(resolution,[status(thm)],[f159,f168]) ).
fof(f172,plain,
apply(sk0_15,sk0_16,sk0_16),
inference(resolution,[status(thm)],[f171,f129]) ).
fof(f181,plain,
member(sk0_16,equivalence_class(sk0_16,sk0_14,sk0_15)),
inference(resolution,[status(thm)],[f172,f167]) ).
fof(f182,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f181,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n029.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 : Mon Apr 29 21:54:19 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.19/0.41 % Refutation found
% 0.19/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42 % Elapsed time: 0.080918 seconds
% 0.19/0.42 % CPU time: 0.521332 seconds
% 0.19/0.42 % Total memory used: 57.503 MB
% 0.19/0.42 % Net memory used: 57.346 MB
%------------------------------------------------------------------------------