TSTP Solution File: BOO015-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO015-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:12:56 EDT 2024
% Result : Unsatisfiable 228.39s 29.12s
% Output : CNFRefutation 230.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 26
% Syntax : Number of formulae : 278 ( 153 unt; 0 def)
% Number of atoms : 533 ( 96 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 511 ( 256 ~; 254 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 596 ( 596 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ product(V1,V2,V4)
| sum(X,V3,V4) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ product(V1,V2,V4)
| sum(V3,X,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : sum(X,inverse(X),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
product(x,y,x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f27,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f30,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f31,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f32,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f33,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f34,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(f35,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)],[f34]) ).
fof(f36,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| product(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
| ~ product(V3,X,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X5,X1,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f42,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(f43,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)],[f42]) ).
fof(f44,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3) )
| ~ product(V1,V2,V4) )
| sum(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X4,X6)
| sum(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f48,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3) )
| ~ product(V1,V2,V4) )
| sum(V3,X,V4) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X3,X5)
| ~ product(X2,X4,X6)
| sum(X5,X1,X6) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f51,plain,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f52,plain,
! [X0] : product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f53,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f54,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
product(x,y,x_times_y),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f59,plain,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f60,plain,
inverse(x_times_y) != x_inverse_plus_y_inverse,
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f61,plain,
sum(inverse(y),inverse(x),x_inverse_plus_y_inverse),
inference(resolution,[status(thm)],[f28,f59]) ).
fof(f63,plain,
product(y,x,x_times_y),
inference(resolution,[status(thm)],[f29,f58]) ).
fof(f66,plain,
! [X0] :
( ~ sum(inverse(x),inverse(y),X0)
| x_inverse_plus_y_inverse = X0 ),
inference(resolution,[status(thm)],[f55,f59]) ).
fof(f67,plain,
! [X0] :
( ~ product(y,x,X0)
| x_times_y = X0 ),
inference(resolution,[status(thm)],[f57,f63]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ product(y,X0,X1)
| ~ sum(x,X0,X2)
| ~ product(y,X2,X3)
| sum(x_times_y,X1,X3) ),
inference(resolution,[status(thm)],[f35,f63]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ~ product(x,X0,X1)
| ~ sum(y,X0,X2)
| ~ sum(x_times_y,X1,X3)
| product(x,X2,X3) ),
inference(resolution,[status(thm)],[f37,f58]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f30,f55]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f31,f55]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(multiplicative_identity,X0,X3)
| ~ product(X3,X1,X4)
| sum(X1,X2,X4) ),
inference(resolution,[status(thm)],[f32,f39]) ).
fof(f89,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(multiplicative_identity,X0,X1)
| ~ sum(X2,X0,X3)
| ~ sum(X2,X1,X4)
| product(multiplicative_identity,X3,X4) ),
inference(resolution,[status(thm)],[f32,f37]) ).
fof(f90,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)],[f32,f35]) ).
fof(f91,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f32,f57]) ).
fof(f101,plain,
! [X0,X1] :
( ~ sum(x,multiplicative_identity,X0)
| ~ product(y,X0,X1)
| sum(x_times_y,y,X1) ),
inference(resolution,[status(thm)],[f33,f69]) ).
fof(f105,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f33,f57]) ).
fof(f107,plain,
x_inverse_plus_y_inverse = add(inverse(x),inverse(y)),
inference(resolution,[status(thm)],[f26,f66]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f26,f55]) ).
fof(f110,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f26,f28]) ).
fof(f112,plain,
x_times_y = multiply(y,x),
inference(resolution,[status(thm)],[f27,f67]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X0,X4)
| ~ product(X4,X1,X5)
| sum(multiply(X3,X1),X2,X5) ),
inference(resolution,[status(thm)],[f27,f39]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ sum(multiply(X0,X3),X2,X5)
| product(X0,X4,X5) ),
inference(resolution,[status(thm)],[f27,f37]) ).
fof(f117,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)],[f27,f35]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f27,f57]) ).
fof(f119,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f27,f29]) ).
fof(f144,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f84,f26]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(multiplicative_identity,X0,X3)
| ~ sum(X1,X2,X4)
| product(X3,X1,X4) ),
inference(resolution,[status(thm)],[f41,f32]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(inverse(X0),X1,X3)
| ~ sum(X0,X3,X4)
| product(multiplicative_identity,X2,X4) ),
inference(resolution,[status(thm)],[f43,f51]) ).
fof(f161,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)],[f43,f31]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X4,X5)
| product(add(X0,X3),X2,X5) ),
inference(resolution,[status(thm)],[f43,f26]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(additive_identity,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X2,X1,X4)
| sum(additive_identity,X3,X4) ),
inference(resolution,[status(thm)],[f45,f30]) ).
fof(f179,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f86,f26]) ).
fof(f181,plain,
inverse(multiplicative_identity) = additive_identity,
inference(resolution,[status(thm)],[f91,f53]) ).
fof(f182,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f91,f27]) ).
fof(f189,plain,
! [X0] : X0 = multiply(X0,multiplicative_identity),
inference(resolution,[status(thm)],[f105,f27]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f110,f55]) ).
fof(f213,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f119,f57]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(additive_identity,X0,X3)
| ~ sum(X3,X1,X4)
| product(X1,X2,X4) ),
inference(resolution,[status(thm)],[f47,f30]) ).
fof(f224,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,additive_identity,X1)
| ~ product(X2,X0,X3)
| ~ sum(X3,additive_identity,X4)
| product(X2,X1,X4) ),
inference(resolution,[status(thm)],[f47,f31]) ).
fof(f227,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(additive_identity,X0,X3)
| ~ product(X1,X2,X4)
| sum(X3,X1,X4) ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f241,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f109,f110]) ).
fof(f274,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(resolution,[status(thm)],[f118,f53]) ).
fof(f276,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f118,f119]) ).
fof(f338,plain,
! [X0,X1] :
( ~ sum(y,inverse(x),X0)
| ~ sum(x_times_y,additive_identity,X1)
| product(x,X0,X1) ),
inference(resolution,[status(thm)],[f81,f53]) ).
fof(f350,plain,
! [X0,X1] :
( ~ sum(multiplicative_identity,x,X0)
| ~ product(X0,y,X1)
| sum(y,x_times_y,X1) ),
inference(resolution,[status(thm)],[f88,f58]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( ~ sum(multiplicative_identity,X0,X1)
| ~ product(X1,X2,X3)
| sum(X2,multiply(X2,X0),X3) ),
inference(resolution,[status(thm)],[f88,f119]) ).
fof(f457,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| product(multiplicative_identity,X2,X3) ),
inference(resolution,[status(thm)],[f89,f32]) ).
fof(f465,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(multiplicative_identity,X2,X3)
| sum(X0,X1,X3) ),
inference(resolution,[status(thm)],[f90,f32]) ).
fof(f657,plain,
! [X0] :
( ~ sum(x,multiplicative_identity,X0)
| sum(x_times_y,y,multiply(X0,y)) ),
inference(resolution,[status(thm)],[f101,f119]) ).
fof(f711,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,inverse(X1),X2)
| ~ product(X2,X1,X3)
| sum(multiply(X0,X1),additive_identity,X3) ),
inference(resolution,[status(thm)],[f115,f52]) ).
fof(f716,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X2,inverse(X1),X3)
| sum(multiply(X0,inverse(X1)),additive_identity,X3) ),
inference(resolution,[status(thm)],[f115,f53]) ).
fof(f719,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ product(X2,X3,X4)
| sum(multiply(X0,X3),multiply(X3,X1),X4) ),
inference(resolution,[status(thm)],[f115,f119]) ).
fof(f731,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,inverse(X1),X2)
| ~ sum(multiply(X1,X0),additive_identity,X3)
| product(X1,X2,X3) ),
inference(resolution,[status(thm)],[f116,f53]) ).
fof(f733,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(multiply(X3,X0),multiply(X1,X3),X4)
| product(X3,X2,X4) ),
inference(resolution,[status(thm)],[f116,f119]) ).
fof(f821,plain,
! [X0,X1,X2] :
( ~ sum(X0,y,X1)
| ~ product(x,X1,X2)
| sum(multiply(x,X0),x_times_y,X2) ),
inference(resolution,[status(thm)],[f117,f58]) ).
fof(f853,plain,
sum(x_times_y,y,multiply(add(multiplicative_identity,x),y)),
inference(resolution,[status(thm)],[f657,f110]) ).
fof(f854,plain,
sum(x_times_y,y,multiply(y,add(multiplicative_identity,x))),
inference(forward_demodulation,[status(thm)],[f276,f853]) ).
fof(f858,plain,
add(y,x_times_y) = multiply(y,add(multiplicative_identity,x)),
inference(resolution,[status(thm)],[f854,f197]) ).
fof(f888,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(multiplicative_identity,add(X1,X0),X2) ),
inference(resolution,[status(thm)],[f457,f110]) ).
fof(f950,plain,
! [X0,X1] : product(multiplicative_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f888,f26]) ).
fof(f976,plain,
! [X0,X1,X2] :
( ~ product(multiplicative_identity,add(X0,X1),X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f950,f57]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f465,f30]) ).
fof(f1146,plain,
! [X0,X1,X2] :
( ~ product(multiplicative_identity,add(X0,X1),X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f465,f26]) ).
fof(f1147,plain,
! [X0,X1] : sum(additive_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f1137,f950]) ).
fof(f1898,plain,
! [X0,X1,X2,X3] :
( ~ product(inverse(X0),X1,X2)
| ~ sum(X0,X2,X3)
| product(multiplicative_identity,add(X1,X0),X3) ),
inference(resolution,[status(thm)],[f160,f110]) ).
fof(f2181,plain,
! [X0,X1,X2] :
( ~ product(additive_identity,additive_identity,X0)
| ~ sum(X1,X0,X2)
| product(X1,X1,X2) ),
inference(resolution,[status(thm)],[f161,f31]) ).
fof(f2198,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X2,X4)
| product(add(X3,X0),add(X1,X3),X4) ),
inference(resolution,[status(thm)],[f162,f110]) ).
fof(f2201,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| sum(additive_identity,X2,X3) ),
inference(resolution,[status(thm)],[f163,f30]) ).
fof(f2254,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| sum(additive_identity,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f2201,f119]) ).
fof(f2334,plain,
! [X0,X1] : sum(additive_identity,multiply(X0,X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f2254,f27]) ).
fof(f2367,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,multiply(X0,X1),X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f2334,f55]) ).
fof(f2368,plain,
! [X0,X1] : sum(multiply(X0,X1),additive_identity,multiply(X1,X0)),
inference(resolution,[status(thm)],[f2334,f28]) ).
fof(f2654,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,X1),additive_identity,X2)
| multiply(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f2368,f55]) ).
fof(f2970,plain,
! [X0,X1,X2] :
( ~ product(additive_identity,additive_identity,X0)
| ~ sum(X0,X1,X2)
| product(X1,X1,X2) ),
inference(resolution,[status(thm)],[f219,f30]) ).
fof(f3605,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ sum(X2,additive_identity,X3)
| product(X0,X1,X3) ),
inference(resolution,[status(thm)],[f224,f31]) ).
fof(f3665,plain,
! [X0,X1,X2,X3] :
( ~ product(additive_identity,X0,X1)
| ~ product(X2,add(X0,X2),X3)
| sum(X1,X2,X3) ),
inference(resolution,[status(thm)],[f227,f26]) ).
fof(f3733,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,X1),additive_identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3605,f27]) ).
fof(f4272,plain,
! [X0,X1] :
( ~ sum(X0,multiply(additive_identity,additive_identity),X1)
| product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2181,f119]) ).
fof(f4281,plain,
! [X0] : product(X0,X0,add(multiply(additive_identity,additive_identity),X0)),
inference(resolution,[status(thm)],[f4272,f110]) ).
fof(f4282,plain,
! [X0] : product(X0,X0,add(X0,multiply(additive_identity,additive_identity))),
inference(resolution,[status(thm)],[f4272,f26]) ).
fof(f4515,plain,
! [X0] : multiply(X0,X0) = add(multiply(additive_identity,additive_identity),X0),
inference(resolution,[status(thm)],[f4281,f213]) ).
fof(f5481,plain,
! [X0] :
( ~ sum(x_times_y,additive_identity,X0)
| product(x,add(inverse(x),y),X0) ),
inference(resolution,[status(thm)],[f338,f110]) ).
fof(f5482,plain,
! [X0] :
( ~ sum(x_times_y,additive_identity,X0)
| product(x,add(y,inverse(x)),X0) ),
inference(forward_demodulation,[status(thm)],[f241,f5481]) ).
fof(f5810,plain,
! [X0,X1] :
( ~ sum(add(multiply(additive_identity,additive_identity),additive_identity),X0,X1)
| product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f2970,f4281]) ).
fof(f5811,plain,
! [X0,X1] :
( ~ sum(multiply(additive_identity,additive_identity),X0,X1)
| product(X0,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f4515,f5810]) ).
fof(f5891,plain,
! [X0] :
( ~ sum(multiplicative_identity,x,X0)
| sum(y,x_times_y,multiply(X0,y)) ),
inference(resolution,[status(thm)],[f350,f27]) ).
fof(f5912,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| sum(X0,multiply(X0,inverse(multiplicative_identity)),X1) ),
inference(resolution,[status(thm)],[f353,f51]) ).
fof(f5913,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| sum(X0,multiply(X0,additive_identity),X1) ),
inference(forward_demodulation,[status(thm)],[f181,f5912]) ).
fof(f5921,plain,
! [X0,X1,X2] :
( ~ product(add(X0,multiplicative_identity),X1,X2)
| sum(X1,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f353,f110]) ).
fof(f5949,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),X0),
inference(resolution,[status(thm)],[f5913,f32]) ).
fof(f5991,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(resolution,[status(thm)],[f5949,f2367]) ).
fof(f6061,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| product(X0,X0,X1) ),
inference(backward_demodulation,[status(thm)],[f5991,f5811]) ).
fof(f6077,plain,
! [X0] : product(X0,X0,add(X0,additive_identity)),
inference(backward_demodulation,[status(thm)],[f5991,f4282]) ).
fof(f6078,plain,
! [X0] : product(X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f179,f6077]) ).
fof(f6233,plain,
! [X0,X1,X2] :
( ~ sum(multiplicative_identity,X0,X1)
| ~ sum(X0,X0,X2)
| product(X1,X0,X2) ),
inference(resolution,[status(thm)],[f6078,f150]) ).
fof(f6651,plain,
! [X0,X1] : product(add(X0,X1),add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f6061,f1147]) ).
fof(f7190,plain,
! [X0,X1] : product(add(X0,X1),add(X1,X0),add(X1,X0)),
inference(paramodulation,[status(thm)],[f241,f6651]) ).
fof(f8685,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| sum(multiply(additive_identity,X0),additive_identity,X1) ),
inference(resolution,[status(thm)],[f711,f30]) ).
fof(f8690,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| sum(multiply(inverse(inverse(X0)),X0),additive_identity,X1) ),
inference(resolution,[status(thm)],[f711,f50]) ).
fof(f8691,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| sum(multiply(X0,inverse(inverse(X0))),additive_identity,X1) ),
inference(forward_demodulation,[status(thm)],[f276,f8690]) ).
fof(f8979,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,inverse(inverse(X0)),X1)
| sum(multiply(X0,inverse(inverse(X0))),additive_identity,X1) ),
inference(resolution,[status(thm)],[f716,f51]) ).
fof(f9011,plain,
! [X0,X1,X2] :
( ~ product(multiplicative_identity,X0,X1)
| sum(multiply(inverse(X2),X0),multiply(X0,X2),X1) ),
inference(resolution,[status(thm)],[f719,f50]) ).
fof(f9189,plain,
! [X0,X1] :
( ~ sum(X0,X0,X1)
| product(add(X0,multiplicative_identity),X0,X1) ),
inference(resolution,[status(thm)],[f6233,f110]) ).
fof(f9197,plain,
! [X0] : product(add(X0,multiplicative_identity),X0,add(X0,X0)),
inference(resolution,[status(thm)],[f9189,f110]) ).
fof(f9283,plain,
! [X0] : multiply(X0,add(X0,multiplicative_identity)) = add(X0,X0),
inference(resolution,[status(thm)],[f9197,f213]) ).
fof(f9318,plain,
! [X0] : multiply(X0,add(multiplicative_identity,X0)) = add(X0,X0),
inference(paramodulation,[status(thm)],[f241,f9283]) ).
fof(f9721,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,X1),additive_identity,X2)
| product(X0,add(inverse(X0),X1),X2) ),
inference(resolution,[status(thm)],[f731,f110]) ).
fof(f10052,plain,
! [X0,X1] :
( ~ sum(multiply(X0,inverse(y)),multiply(inverse(x),X0),X1)
| product(X0,x_inverse_plus_y_inverse,X1) ),
inference(resolution,[status(thm)],[f733,f61]) ).
fof(f12637,plain,
! [X0] : sum(add(multiplicative_identity,X0),multiply(add(multiplicative_identity,X0),X0),add(multiplicative_identity,X0)),
inference(resolution,[status(thm)],[f5921,f7190]) ).
fof(f12638,plain,
! [X0] : sum(add(multiplicative_identity,X0),multiply(X0,add(multiplicative_identity,X0)),add(multiplicative_identity,X0)),
inference(forward_demodulation,[status(thm)],[f276,f12637]) ).
fof(f12639,plain,
! [X0] : sum(add(multiplicative_identity,X0),add(X0,X0),add(multiplicative_identity,X0)),
inference(forward_demodulation,[status(thm)],[f9318,f12638]) ).
fof(f12668,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(add(X1,multiplicative_identity),X0)),
inference(resolution,[status(thm)],[f5921,f27]) ).
fof(f14274,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = multiply(add(X1,multiplicative_identity),X0),
inference(resolution,[status(thm)],[f12668,f197]) ).
fof(f14275,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(add(X1,multiplicative_identity),X0),
inference(forward_demodulation,[status(thm)],[f241,f14274]) ).
fof(f14343,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,multiplicative_identity),X0)),
inference(paramodulation,[status(thm)],[f276,f12668]) ).
fof(f17603,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(add(multiplicative_identity,X1),X0),
inference(paramodulation,[status(thm)],[f241,f14275]) ).
fof(f18307,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(multiplicative_identity,X1),X0)),
inference(paramodulation,[status(thm)],[f241,f14343]) ).
fof(f30757,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| product(multiplicative_identity,add(X0,X0),X1) ),
inference(resolution,[status(thm)],[f1898,f52]) ).
fof(f30935,plain,
! [X0] : product(multiplicative_identity,add(X0,X0),X0),
inference(resolution,[status(thm)],[f30757,f31]) ).
fof(f30948,plain,
! [X0] : sum(X0,X0,X0),
inference(resolution,[status(thm)],[f30935,f1146]) ).
fof(f30950,plain,
! [X0] : add(X0,X0) = X0,
inference(resolution,[status(thm)],[f30935,f976]) ).
fof(f31269,plain,
! [X0,X1] :
( ~ sum(X0,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f30948,f55]) ).
fof(f31392,plain,
! [X0] : sum(add(multiplicative_identity,X0),X0,add(multiplicative_identity,X0)),
inference(backward_demodulation,[status(thm)],[f30950,f12639]) ).
fof(f33243,plain,
! [X0,X1] :
( ~ sum(X0,x_times_y,X1)
| product(add(X0,x),add(y,X0),X1) ),
inference(resolution,[status(thm)],[f2198,f58]) ).
fof(f63778,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f8685,f52]) ).
fof(f63826,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(resolution,[status(thm)],[f63778,f3733]) ).
fof(f64005,plain,
! [X0,X1,X2] :
( ~ product(X0,add(X1,X0),X2)
| sum(additive_identity,X0,X2) ),
inference(resolution,[status(thm)],[f63826,f3665]) ).
fof(f67673,plain,
product(x,add(y,inverse(x)),x_times_y),
inference(resolution,[status(thm)],[f5482,f31]) ).
fof(f68107,plain,
multiply(add(y,inverse(x)),x) = x_times_y,
inference(resolution,[status(thm)],[f67673,f213]) ).
fof(f68108,plain,
multiply(x,add(y,inverse(x))) = x_times_y,
inference(forward_demodulation,[status(thm)],[f276,f68107]) ).
fof(f68495,plain,
! [X0] : sum(additive_identity,multiplicative_identity,add(multiplicative_identity,X0)),
inference(resolution,[status(thm)],[f64005,f950]) ).
fof(f68520,plain,
! [X0,X1] : sum(additive_identity,X0,multiply(add(X1,X0),X0)),
inference(resolution,[status(thm)],[f64005,f119]) ).
fof(f68521,plain,
! [X0,X1] : sum(additive_identity,X0,multiply(X0,add(X1,X0))),
inference(forward_demodulation,[status(thm)],[f276,f68520]) ).
fof(f68561,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f68495,f84]) ).
fof(f68801,plain,
add(y,x_times_y) = multiply(y,multiplicative_identity),
inference(backward_demodulation,[status(thm)],[f68561,f858]) ).
fof(f68802,plain,
add(y,x_times_y) = y,
inference(forward_demodulation,[status(thm)],[f189,f68801]) ).
fof(f68838,plain,
! [X0] : sum(add(multiplicative_identity,X0),X0,multiplicative_identity),
inference(backward_demodulation,[status(thm)],[f68561,f31392]) ).
fof(f68839,plain,
! [X0] : sum(multiplicative_identity,X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f68561,f68838]) ).
fof(f68881,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(multiplicative_identity,X0)),
inference(backward_demodulation,[status(thm)],[f68561,f18307]) ).
fof(f68882,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f182,f68881]) ).
fof(f68885,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(multiplicative_identity,X0),
inference(backward_demodulation,[status(thm)],[f68561,f17603]) ).
fof(f68886,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f182,f68885]) ).
fof(f69211,plain,
sum(y,x_times_y,multiply(multiplicative_identity,y)),
inference(resolution,[status(thm)],[f68839,f5891]) ).
fof(f69212,plain,
sum(y,x_times_y,y),
inference(forward_demodulation,[status(thm)],[f182,f69211]) ).
fof(f73410,plain,
! [X0,X1] : X0 = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f68521,f84]) ).
fof(f73766,plain,
inverse(y) = multiply(inverse(y),x_inverse_plus_y_inverse),
inference(paramodulation,[status(thm)],[f107,f73410]) ).
fof(f73767,plain,
inverse(y) = multiply(x_inverse_plus_y_inverse,inverse(y)),
inference(forward_demodulation,[status(thm)],[f276,f73766]) ).
fof(f73770,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f68886,f73410]) ).
fof(f73771,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f276,f73770]) ).
fof(f73777,plain,
! [X0,X1] : X0 = multiply(X0,add(X0,X1)),
inference(paramodulation,[status(thm)],[f241,f73410]) ).
fof(f73793,plain,
! [X0,X1] : sum(add(X0,X1),X1,add(X0,X1)),
inference(paramodulation,[status(thm)],[f73410,f68882]) ).
fof(f74464,plain,
inverse(x) = multiply(inverse(x),x_inverse_plus_y_inverse),
inference(paramodulation,[status(thm)],[f107,f73777]) ).
fof(f74465,plain,
inverse(x) = multiply(x_inverse_plus_y_inverse,inverse(x)),
inference(forward_demodulation,[status(thm)],[f276,f74464]) ).
fof(f80428,plain,
! [X0,X1] : sum(add(X0,X1),X1,add(X1,X0)),
inference(paramodulation,[status(thm)],[f241,f73793]) ).
fof(f83154,plain,
! [X0,X1,X2] :
( ~ sum(add(X0,X1),X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f80428,f55]) ).
fof(f94712,plain,
x_times_y = multiply(x,y),
inference(forward_demodulation,[status(thm)],[f276,f112]) ).
fof(f96537,plain,
multiply(x,y) = multiply(x,x_times_y),
inference(paramodulation,[status(thm)],[f94712,f73771]) ).
fof(f96538,plain,
x_times_y = multiply(x,x_times_y),
inference(forward_demodulation,[status(thm)],[f94712,f96537]) ).
fof(f96976,plain,
x_times_y = multiply(x_times_y,y),
inference(paramodulation,[status(thm)],[f68802,f73410]) ).
fof(f96977,plain,
x_times_y = multiply(y,x_times_y),
inference(forward_demodulation,[status(thm)],[f276,f96976]) ).
fof(f97275,plain,
sum(x_times_y,y,y),
inference(resolution,[status(thm)],[f69212,f28]) ).
fof(f107844,plain,
! [X0] : sum(multiply(X0,inverse(inverse(X0))),additive_identity,X0),
inference(resolution,[status(thm)],[f8691,f32]) ).
fof(f107935,plain,
! [X0] : multiply(inverse(inverse(X0)),X0) = X0,
inference(resolution,[status(thm)],[f107844,f2654]) ).
fof(f107936,plain,
! [X0] : multiply(X0,inverse(inverse(X0))) = X0,
inference(forward_demodulation,[status(thm)],[f276,f107935]) ).
fof(f110140,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,inverse(inverse(X0)),X1)
| sum(X0,additive_identity,X1) ),
inference(forward_demodulation,[status(thm)],[f107936,f8979]) ).
fof(f110141,plain,
! [X0] : sum(X0,additive_identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f110140,f32]) ).
fof(f110285,plain,
! [X0] : add(additive_identity,X0) = inverse(inverse(add(X0,additive_identity))),
inference(resolution,[status(thm)],[f110141,f83154]) ).
fof(f110286,plain,
! [X0] : X0 = inverse(inverse(add(X0,additive_identity))),
inference(forward_demodulation,[status(thm)],[f144,f110285]) ).
fof(f110287,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f179,f110286]) ).
fof(f110954,plain,
! [X0,X1] : sum(multiply(inverse(X0),X1),multiply(X1,X0),X1),
inference(resolution,[status(thm)],[f9011,f32]) ).
fof(f111157,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X1),X0)) = X0,
inference(resolution,[status(thm)],[f110954,f197]) ).
fof(f111524,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f276,f111157]) ).
fof(f111550,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f276,f111157]) ).
fof(f114457,plain,
! [X0,X1] : product(X0,add(inverse(X0),X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f9721,f2368]) ).
fof(f114941,plain,
! [X0,X1] : multiply(add(inverse(X0),X1),X0) = multiply(X1,X0),
inference(resolution,[status(thm)],[f114457,f213]) ).
fof(f114942,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f276,f114941]) ).
fof(f116291,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(multiply(inverse(X0),X1),X0),
inference(paramodulation,[status(thm)],[f68886,f114942]) ).
fof(f116292,plain,
! [X0,X1] : additive_identity = multiply(multiply(inverse(X0),X1),X0),
inference(forward_demodulation,[status(thm)],[f274,f116291]) ).
fof(f116293,plain,
! [X0,X1] : additive_identity = multiply(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f276,f116292]) ).
fof(f116717,plain,
! [X0,X1] : additive_identity = multiply(inverse(X0),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f110287,f116293]) ).
fof(f117483,plain,
additive_identity = multiply(inverse(x),x_times_y),
inference(paramodulation,[status(thm)],[f68108,f116717]) ).
fof(f117484,plain,
additive_identity = multiply(x_times_y,inverse(x)),
inference(forward_demodulation,[status(thm)],[f276,f117483]) ).
fof(f117489,plain,
additive_identity = multiply(inverse(y),x_times_y),
inference(paramodulation,[status(thm)],[f96977,f116717]) ).
fof(f117490,plain,
additive_identity = multiply(x_times_y,inverse(y)),
inference(forward_demodulation,[status(thm)],[f276,f117489]) ).
fof(f117491,plain,
additive_identity = multiply(inverse(x_inverse_plus_y_inverse),inverse(x)),
inference(paramodulation,[status(thm)],[f74465,f116717]) ).
fof(f117492,plain,
additive_identity = multiply(inverse(x),inverse(x_inverse_plus_y_inverse)),
inference(forward_demodulation,[status(thm)],[f276,f117491]) ).
fof(f117493,plain,
additive_identity = multiply(inverse(x_inverse_plus_y_inverse),inverse(y)),
inference(paramodulation,[status(thm)],[f73767,f116717]) ).
fof(f117494,plain,
additive_identity = multiply(inverse(y),inverse(x_inverse_plus_y_inverse)),
inference(forward_demodulation,[status(thm)],[f276,f117493]) ).
fof(f118224,plain,
! [X0] :
( ~ sum(additive_identity,multiply(inverse(x),x_times_y),X0)
| product(x_times_y,x_inverse_plus_y_inverse,X0) ),
inference(paramodulation,[status(thm)],[f117490,f10052]) ).
fof(f118225,plain,
! [X0] :
( ~ sum(additive_identity,multiply(x_times_y,inverse(x)),X0)
| product(x_times_y,x_inverse_plus_y_inverse,X0) ),
inference(forward_demodulation,[status(thm)],[f276,f118224]) ).
fof(f118226,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| product(x_times_y,x_inverse_plus_y_inverse,X0) ),
inference(forward_demodulation,[status(thm)],[f117484,f118225]) ).
fof(f122021,plain,
! [X0] :
( ~ product(x,y,X0)
| sum(multiply(x,x_times_y),x_times_y,X0) ),
inference(resolution,[status(thm)],[f821,f97275]) ).
fof(f122022,plain,
! [X0] :
( ~ product(x,y,X0)
| sum(x_times_y,x_times_y,X0) ),
inference(forward_demodulation,[status(thm)],[f96538,f122021]) ).
fof(f123779,plain,
add(multiply(x,inverse(x_inverse_plus_y_inverse)),additive_identity) = inverse(x_inverse_plus_y_inverse),
inference(paramodulation,[status(thm)],[f117492,f111524]) ).
fof(f123780,plain,
multiply(x,inverse(x_inverse_plus_y_inverse)) = inverse(x_inverse_plus_y_inverse),
inference(forward_demodulation,[status(thm)],[f179,f123779]) ).
fof(f124166,plain,
add(multiply(y,inverse(x_inverse_plus_y_inverse)),additive_identity) = inverse(x_inverse_plus_y_inverse),
inference(paramodulation,[status(thm)],[f117494,f111524]) ).
fof(f124167,plain,
multiply(y,inverse(x_inverse_plus_y_inverse)) = inverse(x_inverse_plus_y_inverse),
inference(forward_demodulation,[status(thm)],[f179,f124166]) ).
fof(f143676,plain,
add(x,inverse(x_inverse_plus_y_inverse)) = x,
inference(paramodulation,[status(thm)],[f123780,f68886]) ).
fof(f145135,plain,
add(y,inverse(x_inverse_plus_y_inverse)) = y,
inference(paramodulation,[status(thm)],[f124167,f68886]) ).
fof(f151181,plain,
( spl0_380
<=> sum(x_times_y,x_times_y,inverse(x_inverse_plus_y_inverse)) ),
introduced(split_symbol_definition) ).
fof(f151182,plain,
( sum(x_times_y,x_times_y,inverse(x_inverse_plus_y_inverse))
| ~ spl0_380 ),
inference(component_clause,[status(thm)],[f151181]) ).
fof(f151183,plain,
( ~ sum(x_times_y,x_times_y,inverse(x_inverse_plus_y_inverse))
| spl0_380 ),
inference(component_clause,[status(thm)],[f151181]) ).
fof(f178551,plain,
product(x_times_y,x_inverse_plus_y_inverse,additive_identity),
inference(resolution,[status(thm)],[f118226,f30]) ).
fof(f178648,plain,
multiply(x_inverse_plus_y_inverse,x_times_y) = additive_identity,
inference(resolution,[status(thm)],[f178551,f213]) ).
fof(f178649,plain,
multiply(x_times_y,x_inverse_plus_y_inverse) = additive_identity,
inference(forward_demodulation,[status(thm)],[f276,f178648]) ).
fof(f178703,plain,
add(additive_identity,multiply(x_times_y,inverse(x_inverse_plus_y_inverse))) = x_times_y,
inference(paramodulation,[status(thm)],[f178649,f111550]) ).
fof(f178704,plain,
multiply(x_times_y,inverse(x_inverse_plus_y_inverse)) = x_times_y,
inference(forward_demodulation,[status(thm)],[f144,f178703]) ).
fof(f179294,plain,
sum(inverse(x_inverse_plus_y_inverse),x_times_y,inverse(x_inverse_plus_y_inverse)),
inference(paramodulation,[status(thm)],[f178704,f68882]) ).
fof(f190220,plain,
( x_times_y = inverse(x_inverse_plus_y_inverse)
| ~ spl0_380 ),
inference(resolution,[status(thm)],[f151182,f31269]) ).
fof(f190426,plain,
( x_inverse_plus_y_inverse = inverse(x_times_y)
| ~ spl0_380 ),
inference(paramodulation,[status(thm)],[f190220,f110287]) ).
fof(f190427,plain,
( $false
| ~ spl0_380 ),
inference(forward_subsumption_resolution,[status(thm)],[f190426,f60]) ).
fof(f190428,plain,
~ spl0_380,
inference(contradiction_clause,[status(thm)],[f190427]) ).
fof(f239285,plain,
product(add(inverse(x_inverse_plus_y_inverse),x),add(y,inverse(x_inverse_plus_y_inverse)),inverse(x_inverse_plus_y_inverse)),
inference(resolution,[status(thm)],[f33243,f179294]) ).
fof(f239286,plain,
product(add(x,inverse(x_inverse_plus_y_inverse)),add(y,inverse(x_inverse_plus_y_inverse)),inverse(x_inverse_plus_y_inverse)),
inference(forward_demodulation,[status(thm)],[f241,f239285]) ).
fof(f239287,plain,
product(x,add(y,inverse(x_inverse_plus_y_inverse)),inverse(x_inverse_plus_y_inverse)),
inference(forward_demodulation,[status(thm)],[f143676,f239286]) ).
fof(f239288,plain,
product(x,y,inverse(x_inverse_plus_y_inverse)),
inference(forward_demodulation,[status(thm)],[f145135,f239287]) ).
fof(f239309,plain,
sum(x_times_y,x_times_y,inverse(x_inverse_plus_y_inverse)),
inference(resolution,[status(thm)],[f239288,f122022]) ).
fof(f239310,plain,
( $false
| spl0_380 ),
inference(forward_subsumption_resolution,[status(thm)],[f239309,f151183]) ).
fof(f239311,plain,
spl0_380,
inference(contradiction_clause,[status(thm)],[f239310]) ).
fof(f239312,plain,
$false,
inference(sat_refutation,[status(thm)],[f190428,f239311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : BOO015-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 22:39:01 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.6.0
% 228.39/29.12 % Refutation found
% 228.39/29.12 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 228.39/29.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 230.46/29.45 % Elapsed time: 29.080183 seconds
% 230.46/29.45 % CPU time: 230.014029 seconds
% 230.46/29.45 % Total memory used: 1.060 GB
% 230.46/29.45 % Net memory used: 1.005 GB
%------------------------------------------------------------------------------