TSTP Solution File: BOO009-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 12:02:44 EDT 2023
% Result : Unsatisfiable 1.44s 0.65s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 21 unt; 0 def)
% Number of atoms : 86 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 115 (; 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ product(x,add(x,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f29,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f32,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ product(X,V3,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f44,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3) )
| ~ sum(V3,X,V4) )
| product(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X3,X5)
| ~ sum(X5,X1,X6)
| product(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f52,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f56,plain,
~ product(x,add(x,y),x),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f58,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f122,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X1,inverse(X0),inverse(X0))
| sum(X2,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f33,f51]) ).
fof(f216,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f53,f29]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X1,X0) ),
inference(resolution,[status(thm)],[f53,f122]) ).
fof(f234,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f217,f29]) ).
fof(f539,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X0,X3,X3)
| product(X2,add(X3,X1),add(X3,X1)) ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f1277,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f127,f28]) ).
fof(f1440,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f1277,f58]) ).
fof(f1444,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f1440,f216]) ).
fof(f1491,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1444,f58]) ).
fof(f1522,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,add(additive_identity,X1),add(additive_identity,X1)) ),
inference(resolution,[status(thm)],[f1491,f539]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X1,add(additive_identity,X1)) ),
inference(forward_demodulation,[status(thm)],[f234,f1522]) ).
fof(f1524,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X1,X1) ),
inference(forward_demodulation,[status(thm)],[f234,f1523]) ).
fof(f1616,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f1524,f122]) ).
fof(f1704,plain,
! [X0,X1] : product(X0,add(X0,X1),X0),
inference(resolution,[status(thm)],[f1616,f27]) ).
fof(f1871,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n010.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 10:33:07 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 1.44/0.65 % Refutation found
% 1.44/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.44/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.05/0.67 % Elapsed time: 0.337467 seconds
% 2.05/0.67 % CPU time: 2.096006 seconds
% 2.05/0.67 % Memory used: 28.430 MB
%------------------------------------------------------------------------------