TSTP Solution File: BOO008-1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 67.11s 8.84s
% Output : CNFRefutation 67.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 164 ( 97 unt; 0 def)
% Number of atoms : 305 ( 61 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 284 ( 143 ~; 141 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 308 (; 308 !; 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(f7,axiom,
! [X] : product(multiplicative_identity,X,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(f12,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(V3,X,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ sum(X,V3,V4)
| product(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,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f32,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f33,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f34,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f42,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(V3,X,V4) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ sum(X2,X4,X6)
| product(X5,X1,X6) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3) )
| ~ sum(X,V3,V4) )
| product(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ sum(X0,X5,X6)
| product(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f48,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(f49,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)],[f48]) ).
fof(f55,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f56,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f60,plain,
sum(y,z,y_plus_z),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f61,plain,
sum(x,y_plus_z,x__plus_y_plus_z),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f62,plain,
sum(x,y,x_plus_y),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f63,plain,
sum(x_plus_y,z,x_plus_y__plus_z),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f64,plain,
x__plus_y_plus_z != x_plus_y__plus_z,
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f65,plain,
sum(z,y,y_plus_z),
inference(resolution,[status(thm)],[f30,f60]) ).
fof(f68,plain,
sum(z,x_plus_y,x_plus_y__plus_z),
inference(resolution,[status(thm)],[f30,f63]) ).
fof(f69,plain,
sum(y,x,x_plus_y),
inference(resolution,[status(thm)],[f30,f62]) ).
fof(f70,plain,
sum(y_plus_z,x,x__plus_y_plus_z),
inference(resolution,[status(thm)],[f30,f61]) ).
fof(f73,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f83,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f85,plain,
! [X0] :
( ~ sum(y_plus_z,x,X0)
| x__plus_y_plus_z = X0 ),
inference(resolution,[status(thm)],[f57,f70]) ).
fof(f86,plain,
! [X0] :
( ~ sum(z,y,X0)
| y_plus_z = X0 ),
inference(resolution,[status(thm)],[f57,f65]) ).
fof(f87,plain,
! [X0] :
( ~ sum(z,x_plus_y,X0)
| x_plus_y__plus_z = X0 ),
inference(resolution,[status(thm)],[f57,f68]) ).
fof(f88,plain,
! [X0] :
( ~ sum(y,x,X0)
| x_plus_y = X0 ),
inference(resolution,[status(thm)],[f57,f69]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f57,f73]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f57,f28]) ).
fof(f113,plain,
x__plus_y_plus_z = add(x,y_plus_z),
inference(resolution,[status(thm)],[f85,f73]) ).
fof(f120,plain,
y_plus_z = add(z,y),
inference(resolution,[status(thm)],[f86,f28]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(multiplicative_identity,X0,X1)
| ~ sum(X2,X0,X3)
| ~ product(multiplicative_identity,X3,X4)
| sum(X2,X1,X4) ),
inference(resolution,[status(thm)],[f37,f34]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(inverse(X0),X1,X3)
| ~ product(X0,X3,X4)
| sum(additive_identity,X2,X4) ),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X4,X5)
| sum(multiply(X0,X3),X2,X5) ),
inference(resolution,[status(thm)],[f37,f29]) ).
fof(f139,plain,
x_plus_y__plus_z = add(x_plus_y,z),
inference(resolution,[status(thm)],[f87,f73]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X0,X4)
| ~ sum(multiply(X3,X1),X2,X5)
| product(X4,X1,X5) ),
inference(resolution,[status(thm)],[f43,f29]) ).
fof(f159,plain,
x_plus_y = add(x,y),
inference(resolution,[status(thm)],[f88,f73]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( ~ sum(y,X0,X1)
| ~ product(z,X0,X2)
| ~ sum(y,X2,X3)
| product(y_plus_z,X1,X3) ),
inference(resolution,[status(thm)],[f45,f60]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(additive_identity,X0,X1)
| ~ product(X2,X0,X3)
| ~ sum(additive_identity,X3,X4)
| product(X2,X1,X4) ),
inference(resolution,[status(thm)],[f45,f32]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( ~ sum(x,X0,X1)
| ~ product(y,X0,X2)
| ~ sum(x,X2,X3)
| product(x_plus_y,X1,X3) ),
inference(resolution,[status(thm)],[f45,f62]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( ~ sum(x,X0,X1)
| ~ product(y_plus_z,X0,X2)
| ~ sum(x,X2,X3)
| product(x__plus_y_plus_z,X1,X3) ),
inference(resolution,[status(thm)],[f45,f61]) ).
fof(f194,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(additive_identity,X1,X3)
| ~ sum(X0,X3,X4)
| product(X0,X2,X4) ),
inference(resolution,[status(thm)],[f45,f33]) ).
fof(f218,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f97,f28]) ).
fof(f265,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f59,f34]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f59,f83]) ).
fof(f269,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f59,f29]) ).
fof(f314,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f268,f29]) ).
fof(f336,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,z,X1)
| ~ product(x_plus_y,X0,X2)
| ~ sum(X2,z,X3)
| product(x_plus_y__plus_z,X1,X3) ),
inference(resolution,[status(thm)],[f49,f63]) ).
fof(f372,plain,
! [X0,X1] :
( ~ product(y_plus_z,y,X0)
| ~ sum(x,X0,X1)
| product(x__plus_y_plus_z,x_plus_y,X1) ),
inference(resolution,[status(thm)],[f192,f62]) ).
fof(f485,plain,
! [X0] :
( ~ sum(x,multiply(y,y_plus_z),X0)
| product(x__plus_y_plus_z,x_plus_y,X0) ),
inference(resolution,[status(thm)],[f372,f83]) ).
fof(f488,plain,
product(x__plus_y_plus_z,x_plus_y,add(multiply(y,y_plus_z),x)),
inference(resolution,[status(thm)],[f485,f73]) ).
fof(f489,plain,
product(x__plus_y_plus_z,x_plus_y,add(x,multiply(y,y_plus_z))),
inference(forward_demodulation,[status(thm)],[f218,f488]) ).
fof(f500,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(multiplicative_identity,X2,X3)
| sum(X0,X1,X3) ),
inference(resolution,[status(thm)],[f122,f34]) ).
fof(f513,plain,
! [X0,X1,X2,X3] :
( ~ sum(inverse(X0),X1,X2)
| ~ product(X0,X2,X3)
| sum(additive_identity,multiply(X1,X0),X3) ),
inference(resolution,[status(thm)],[f123,f83]) ).
fof(f516,plain,
multiply(x__plus_y_plus_z,x_plus_y) = add(x,multiply(y,y_plus_z)),
inference(resolution,[status(thm)],[f489,f269]) ).
fof(f529,plain,
! [X0,X1] :
( ~ product(x_plus_y,y,X0)
| ~ sum(X0,z,X1)
| product(x_plus_y__plus_z,y_plus_z,X1) ),
inference(resolution,[status(thm)],[f336,f60]) ).
fof(f607,plain,
! [X0,X1,X2] :
( ~ product(multiplicative_identity,add(X0,X1),X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f500,f28]) ).
fof(f733,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(X3,X2,X4)
| sum(multiply(X3,X0),multiply(X1,X3),X4) ),
inference(resolution,[status(thm)],[f126,f83]) ).
fof(f1393,plain,
! [X0] :
( ~ sum(multiply(y,x_plus_y),z,X0)
| product(x_plus_y__plus_z,y_plus_z,X0) ),
inference(resolution,[status(thm)],[f529,f83]) ).
fof(f1396,plain,
product(x_plus_y__plus_z,y_plus_z,add(z,multiply(y,x_plus_y))),
inference(resolution,[status(thm)],[f1393,f73]) ).
fof(f1416,plain,
multiply(x_plus_y__plus_z,y_plus_z) = add(z,multiply(y,x_plus_y)),
inference(resolution,[status(thm)],[f1396,f269]) ).
fof(f1417,plain,
multiply(y_plus_z,x_plus_y__plus_z) = add(z,multiply(y,x_plus_y)),
inference(forward_demodulation,[status(thm)],[f314,f1416]) ).
fof(f2575,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,multiplicative_identity,X1)
| ~ sum(multiply(X0,X2),X2,X3)
| product(X1,X2,X3) ),
inference(resolution,[status(thm)],[f154,f34]) ).
fof(f2585,plain,
! [X0,X1] :
( ~ product(z,additive_identity,X0)
| ~ sum(y,X0,X1)
| product(y_plus_z,y,X1) ),
inference(resolution,[status(thm)],[f187,f33]) ).
fof(f2849,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ sum(additive_identity,X2,X3)
| product(X0,X1,X3) ),
inference(resolution,[status(thm)],[f189,f32]) ).
fof(f2868,plain,
! [X0,X1] :
( ~ product(y,additive_identity,X0)
| ~ sum(x,X0,X1)
| product(x_plus_y,x,X1) ),
inference(resolution,[status(thm)],[f191,f33]) ).
fof(f3208,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,multiply(X0,X1),X2)
| product(X1,X0,X2) ),
inference(resolution,[status(thm)],[f2849,f83]) ).
fof(f3209,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f2849,f29]) ).
fof(f3313,plain,
! [X0,X1] :
( ~ product(additive_identity,y,X0)
| ~ sum(z,X0,X1)
| product(z,y_plus_z,X1) ),
inference(resolution,[status(thm)],[f194,f65]) ).
fof(f3315,plain,
! [X0,X1] :
( ~ product(additive_identity,x,X0)
| ~ sum(y,X0,X1)
| product(y,x_plus_y,X1) ),
inference(resolution,[status(thm)],[f194,f69]) ).
fof(f3332,plain,
! [X0,X1,X2,X3] :
( ~ product(additive_identity,X0,X1)
| ~ sum(X2,X1,X3)
| product(X2,add(X0,X2),X3) ),
inference(resolution,[status(thm)],[f194,f73]) ).
fof(f11095,plain,
! [X0,X1] :
( ~ product(X0,inverse(X0),X1)
| sum(additive_identity,multiply(additive_identity,X0),X1) ),
inference(resolution,[status(thm)],[f513,f33]) ).
fof(f11994,plain,
! [X0,X1] :
( ~ product(X0,x__plus_y_plus_z,X1)
| sum(multiply(X0,y_plus_z),multiply(x,X0),X1) ),
inference(resolution,[status(thm)],[f733,f70]) ).
fof(f11998,plain,
! [X0,X1] :
( ~ product(X0,x_plus_y__plus_z,X1)
| sum(multiply(X0,z),multiply(x_plus_y,X0),X1) ),
inference(resolution,[status(thm)],[f733,f68]) ).
fof(f13874,plain,
! [X0] : sum(multiply(X0,y_plus_z),multiply(x,X0),multiply(x__plus_y_plus_z,X0)),
inference(resolution,[status(thm)],[f11994,f83]) ).
fof(f14412,plain,
! [X0] : add(multiply(X0,y_plus_z),multiply(x,X0)) = multiply(x__plus_y_plus_z,X0),
inference(resolution,[status(thm)],[f13874,f98]) ).
fof(f14427,plain,
! [X0] : sum(multiply(y_plus_z,X0),multiply(x,X0),multiply(x__plus_y_plus_z,X0)),
inference(paramodulation,[status(thm)],[f314,f13874]) ).
fof(f14939,plain,
! [X0] : add(multiply(y_plus_z,X0),multiply(x,X0)) = multiply(x__plus_y_plus_z,X0),
inference(paramodulation,[status(thm)],[f314,f14412]) ).
fof(f16528,plain,
! [X0] : sum(multiply(y_plus_z,X0),multiply(X0,x),multiply(x__plus_y_plus_z,X0)),
inference(paramodulation,[status(thm)],[f314,f14427]) ).
fof(f17909,plain,
! [X0] : add(multiply(X0,x),multiply(y_plus_z,X0)) = multiply(x__plus_y_plus_z,X0),
inference(resolution,[status(thm)],[f16528,f97]) ).
fof(f27482,plain,
! [X0] : sum(multiply(X0,z),multiply(x_plus_y,X0),multiply(x_plus_y__plus_z,X0)),
inference(resolution,[status(thm)],[f11998,f83]) ).
fof(f27483,plain,
! [X0] : sum(multiply(X0,z),multiply(x_plus_y,X0),multiply(X0,x_plus_y__plus_z)),
inference(resolution,[status(thm)],[f11998,f29]) ).
fof(f27999,plain,
! [X0] : sum(multiply(z,X0),multiply(x_plus_y,X0),multiply(x_plus_y__plus_z,X0)),
inference(paramodulation,[status(thm)],[f314,f27482]) ).
fof(f28996,plain,
! [X0] : sum(multiply(z,X0),multiply(x_plus_y,X0),multiply(X0,x_plus_y__plus_z)),
inference(paramodulation,[status(thm)],[f314,f27483]) ).
fof(f30682,plain,
! [X0] : sum(multiply(z,X0),multiply(X0,x_plus_y),multiply(x_plus_y__plus_z,X0)),
inference(paramodulation,[status(thm)],[f314,f27999]) ).
fof(f31154,plain,
! [X0] : sum(multiply(z,X0),multiply(X0,x_plus_y),multiply(X0,x_plus_y__plus_z)),
inference(paramodulation,[status(thm)],[f314,f28996]) ).
fof(f32711,plain,
! [X0] : add(multiply(X0,x_plus_y),multiply(z,X0)) = multiply(x_plus_y__plus_z,X0),
inference(resolution,[status(thm)],[f30682,f97]) ).
fof(f35614,plain,
! [X0] : sum(additive_identity,multiply(additive_identity,X0),additive_identity),
inference(resolution,[status(thm)],[f11095,f55]) ).
fof(f35624,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(resolution,[status(thm)],[f35614,f3209]) ).
fof(f35625,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f35614,f3208]) ).
fof(f36180,plain,
! [X0] :
( ~ sum(x,additive_identity,X0)
| product(x_plus_y,x,X0) ),
inference(resolution,[status(thm)],[f35625,f2868]) ).
fof(f36253,plain,
! [X0] :
( ~ sum(y,additive_identity,X0)
| product(y_plus_z,y,X0) ),
inference(resolution,[status(thm)],[f35625,f2585]) ).
fof(f37946,plain,
! [X0] :
( ~ sum(z,additive_identity,X0)
| product(z,y_plus_z,X0) ),
inference(resolution,[status(thm)],[f3313,f35624]) ).
fof(f38239,plain,
! [X0] :
( ~ sum(y,additive_identity,X0)
| product(y,x_plus_y,X0) ),
inference(resolution,[status(thm)],[f3315,f35624]) ).
fof(f38321,plain,
! [X0,X1,X2] :
( ~ sum(X0,additive_identity,X1)
| product(X0,add(X2,X0),X1) ),
inference(resolution,[status(thm)],[f3332,f35624]) ).
fof(f42043,plain,
product(x_plus_y,x,x),
inference(resolution,[status(thm)],[f36180,f33]) ).
fof(f42124,plain,
multiply(x_plus_y,x) = x,
inference(resolution,[status(thm)],[f42043,f269]) ).
fof(f42125,plain,
multiply(x,x_plus_y) = x,
inference(forward_demodulation,[status(thm)],[f314,f42124]) ).
fof(f42239,plain,
sum(multiply(z,x),x,multiply(x,x_plus_y__plus_z)),
inference(paramodulation,[status(thm)],[f42125,f31154]) ).
fof(f42507,plain,
product(y_plus_z,y,y),
inference(resolution,[status(thm)],[f36253,f33]) ).
fof(f42594,plain,
multiply(y_plus_z,y) = y,
inference(resolution,[status(thm)],[f42507,f269]) ).
fof(f42595,plain,
multiply(y,y_plus_z) = y,
inference(forward_demodulation,[status(thm)],[f314,f42594]) ).
fof(f42612,plain,
multiply(x__plus_y_plus_z,x_plus_y) = add(x,y),
inference(backward_demodulation,[status(thm)],[f42595,f516]) ).
fof(f42613,plain,
multiply(x__plus_y_plus_z,x_plus_y) = x_plus_y,
inference(forward_demodulation,[status(thm)],[f159,f42612]) ).
fof(f42921,plain,
add(x_plus_y,multiply(z,x__plus_y_plus_z)) = multiply(x_plus_y__plus_z,x__plus_y_plus_z),
inference(paramodulation,[status(thm)],[f42613,f32711]) ).
fof(f42922,plain,
add(x_plus_y,multiply(z,x__plus_y_plus_z)) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
inference(forward_demodulation,[status(thm)],[f314,f42921]) ).
fof(f44230,plain,
product(z,y_plus_z,z),
inference(resolution,[status(thm)],[f37946,f33]) ).
fof(f44318,plain,
multiply(z,y_plus_z) = z,
inference(resolution,[status(thm)],[f44230,f269]) ).
fof(f45068,plain,
product(y,x_plus_y,y),
inference(resolution,[status(thm)],[f38239,f33]) ).
fof(f45154,plain,
multiply(y,x_plus_y) = y,
inference(resolution,[status(thm)],[f45068,f269]) ).
fof(f45172,plain,
multiply(y_plus_z,x_plus_y__plus_z) = add(z,y),
inference(backward_demodulation,[status(thm)],[f45154,f1417]) ).
fof(f45173,plain,
multiply(y_plus_z,x_plus_y__plus_z) = y_plus_z,
inference(forward_demodulation,[status(thm)],[f120,f45172]) ).
fof(f46872,plain,
! [X0,X1] : product(X0,add(X1,X0),X0),
inference(resolution,[status(thm)],[f38321,f33]) ).
fof(f46991,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f46872,f607]) ).
fof(f47048,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
inference(resolution,[status(thm)],[f46872,f269]) ).
fof(f48063,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,X1),X1,X2)
| product(multiplicative_identity,X1,X2) ),
inference(resolution,[status(thm)],[f46991,f2575]) ).
fof(f57209,plain,
product(multiplicative_identity,x,multiply(x,x_plus_y__plus_z)),
inference(resolution,[status(thm)],[f48063,f42239]) ).
fof(f57219,plain,
! [X0,X1] : product(multiplicative_identity,X0,add(X0,multiply(X1,X0))),
inference(resolution,[status(thm)],[f48063,f73]) ).
fof(f57307,plain,
x = multiply(x,x_plus_y__plus_z),
inference(resolution,[status(thm)],[f57209,f265]) ).
fof(f57454,plain,
add(multiply(y_plus_z,x_plus_y__plus_z),x) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
inference(paramodulation,[status(thm)],[f57307,f14939]) ).
fof(f57455,plain,
add(x,multiply(y_plus_z,x_plus_y__plus_z)) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
inference(forward_demodulation,[status(thm)],[f218,f57454]) ).
fof(f57456,plain,
add(x,y_plus_z) = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
inference(forward_demodulation,[status(thm)],[f45173,f57455]) ).
fof(f57457,plain,
x__plus_y_plus_z = multiply(x__plus_y_plus_z,x_plus_y__plus_z),
inference(forward_demodulation,[status(thm)],[f113,f57456]) ).
fof(f57652,plain,
add(x_plus_y,multiply(z,x__plus_y_plus_z)) = x__plus_y_plus_z,
inference(backward_demodulation,[status(thm)],[f57457,f42922]) ).
fof(f58335,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(resolution,[status(thm)],[f57219,f265]) ).
fof(f58760,plain,
! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f314,f58335]) ).
fof(f58861,plain,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f58335,f47048]) ).
fof(f58862,plain,
! [X0,X1] : multiply(X0,multiply(X1,X0)) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f314,f58861]) ).
fof(f66345,plain,
! [X0] : add(multiply(multiply(X0,y_plus_z),x),multiply(X0,y_plus_z)) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
inference(paramodulation,[status(thm)],[f58862,f17909]) ).
fof(f66346,plain,
! [X0] : add(multiply(X0,y_plus_z),multiply(multiply(X0,y_plus_z),x)) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
inference(forward_demodulation,[status(thm)],[f218,f66345]) ).
fof(f66347,plain,
! [X0] : multiply(X0,y_plus_z) = multiply(x__plus_y_plus_z,multiply(X0,y_plus_z)),
inference(forward_demodulation,[status(thm)],[f58760,f66346]) ).
fof(f88070,plain,
multiply(z,y_plus_z) = multiply(x__plus_y_plus_z,z),
inference(paramodulation,[status(thm)],[f44318,f66347]) ).
fof(f88071,plain,
z = multiply(x__plus_y_plus_z,z),
inference(forward_demodulation,[status(thm)],[f44318,f88070]) ).
fof(f88072,plain,
z = multiply(z,x__plus_y_plus_z),
inference(forward_demodulation,[status(thm)],[f314,f88071]) ).
fof(f88334,plain,
add(x_plus_y,z) = x__plus_y_plus_z,
inference(backward_demodulation,[status(thm)],[f88072,f57652]) ).
fof(f88335,plain,
x_plus_y__plus_z = x__plus_y_plus_z,
inference(forward_demodulation,[status(thm)],[f139,f88334]) ).
fof(f88336,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f88335,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:01:48 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 67.11/8.84 % Refutation found
% 67.11/8.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 67.11/8.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 68.36/8.93 % Elapsed time: 8.575099 seconds
% 68.36/8.93 % CPU time: 68.011506 seconds
% 68.36/8.93 % Memory used: 371.772 MB
%------------------------------------------------------------------------------