TSTP Solution File: BOO010-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 20:12:53 EDT 2024
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 36 unt; 0 def)
% Number of atoms : 112 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 104 ( 53 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 151 ( 151 !; 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(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_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(f22,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ sum(x,multiply(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(f30,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f31,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
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(f54,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
~ sum(x,multiply(x,y),x),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f58,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f58,f53]) ).
fof(f62,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(resolution,[status(thm)],[f24,f59]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X0,X1) ),
inference(resolution,[status(thm)],[f24,f53]) ).
fof(f64,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f26]) ).
fof(f116,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f27,f25]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X3)
| sum(X2,multiply(X3,X0),multiply(X3,X0)) ),
inference(resolution,[status(thm)],[f33,f116]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X1)
| sum(multiply(X0,X2),multiply(X1,X2),multiply(X1,X2)) ),
inference(resolution,[status(thm)],[f136,f116]) ).
fof(f204,plain,
! [X0,X1] : sum(multiply(additive_identity,X0),multiply(X1,X0),multiply(X1,X0)),
inference(resolution,[status(thm)],[f174,f28]) ).
fof(f210,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(additive_identity,X1),multiply(X0,X1)),
inference(resolution,[status(thm)],[f204,f63]) ).
fof(f245,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f55,f30]) ).
fof(f247,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| X2 = multiply(X1,X0) ),
inference(resolution,[status(thm)],[f55,f116]) ).
fof(f252,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(resolution,[status(thm)],[f245,f25]) ).
fof(f452,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[f248,f51]) ).
fof(f454,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f248,f25]) ).
fof(f525,plain,
! [X0] : multiply(inverse(X0),X0) = add(multiply(additive_identity,X0),additive_identity),
inference(paramodulation,[status(thm)],[f452,f210]) ).
fof(f526,plain,
! [X0] : additive_identity = add(multiply(additive_identity,X0),additive_identity),
inference(forward_demodulation,[status(thm)],[f452,f525]) ).
fof(f527,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f62,f526]) ).
fof(f545,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f527,f116]) ).
fof(f672,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| ~ product(X0,additive_identity,additive_identity)
| product(X2,X1,X1) ),
inference(resolution,[status(thm)],[f45,f28]) ).
fof(f673,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f545]) ).
fof(f750,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f673,f64]) ).
fof(f795,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f750,f247]) ).
fof(f834,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f795,f64]) ).
fof(f860,plain,
! [X0,X1] : sum(multiply(X0,X1),multiply(multiplicative_identity,X1),multiply(multiplicative_identity,X1)),
inference(resolution,[status(thm)],[f834,f174]) ).
fof(f861,plain,
! [X0,X1] : sum(multiply(X0,X1),X1,multiply(multiplicative_identity,X1)),
inference(forward_demodulation,[status(thm)],[f252,f860]) ).
fof(f862,plain,
! [X0,X1] : sum(multiply(X0,X1),X1,X1),
inference(forward_demodulation,[status(thm)],[f252,f861]) ).
fof(f1061,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),X0),
inference(resolution,[status(thm)],[f862,f26]) ).
fof(f1225,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f454,f1061]) ).
fof(f1338,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : BOO010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 22:27:12 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.6.0
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.45 % Elapsed time: 0.146532 seconds
% 0.15/0.45 % CPU time: 1.092412 seconds
% 0.15/0.45 % Total memory used: 31.798 MB
% 0.15/0.45 % Net memory used: 29.703 MB
%------------------------------------------------------------------------------