TSTP Solution File: RNG008-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:37:41 EDT 2024
% Result : Unsatisfiable 34.32s 4.66s
% Output : CNFRefutation 34.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 17
% Syntax : Number of formulae : 158 ( 103 unt; 0 def)
% Number of atoms : 270 ( 59 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 226 ( 114 ~; 112 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 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 : 384 ( 384 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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(f14,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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(f16,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X,V,W] :
( ! [U,Z] :
( ! [Y] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
| ~ sum(U,Z,W) )
| sum(X,V,W) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| sum(X0,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f34,plain,
! [U,Z,W] :
( ! [X,V] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(X,V,W) )
| product(U,Z,W) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
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)],[f12]) ).
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(f40,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)],[f14]) ).
fof(f41,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)],[f40]) ).
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)],[f15]) ).
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,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f49,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f50,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f51,plain,
! [X0] :
( ~ product(a,b,X0)
| c = X0 ),
inference(resolution,[status(thm)],[f47,f49]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f47,f48]) ).
fof(f72,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f23,f51]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X2,X4)
| product(multiply(X3,X0),X1,X4) ),
inference(resolution,[status(thm)],[f23,f35]) ).
fof(f79,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f23,f52]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f23,f47]) ).
fof(f88,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f93,plain,
! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| additive_identity = X1 ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f96,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f45,f88]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f99,plain,
additive_inverse(additive_identity) = additive_identity,
inference(resolution,[status(thm)],[f94,f26]) ).
fof(f100,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f94,f88]) ).
fof(f101,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f94,f24]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(additive_identity,X1,X3)
| sum(additive_inverse(X0),X2,X3) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(add(X3,X0),X1,X4)
| sum(X3,X2,X4) ),
inference(resolution,[status(thm)],[f28,f24]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X0,X1,X3)
| ~ product(X0,X3,X4)
| sum(X0,X2,X4) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,multiply(X1,X2),X3)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f76,f23]) ).
fof(f299,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(resolution,[status(thm)],[f93,f24]) ).
fof(f319,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f97,f24]) ).
fof(f405,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X0,X3)
| ~ product(X3,X1,X4)
| sum(X1,X2,X4) ),
inference(resolution,[status(thm)],[f41,f48]) ).
fof(f412,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X0,X3)
| ~ sum(X1,X2,X4)
| product(X3,X1,X4) ),
inference(resolution,[status(thm)],[f43,f48]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X0,X2,X3)
| sum(X0,multiply(X0,X1),X3) ),
inference(resolution,[status(thm)],[f119,f23]) ).
fof(f549,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(additive_inverse(X0)),additive_identity,X1) ),
inference(resolution,[status(thm)],[f104,f25]) ).
fof(f553,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X2),add(X0,X2),X1) ),
inference(resolution,[status(thm)],[f104,f88]) ).
fof(f777,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X2,X0,X3)
| sum(X0,multiply(X1,X0),X3) ),
inference(resolution,[status(thm)],[f405,f23]) ).
fof(f974,plain,
! [X0,X1,X2,X3] :
( ~ sum(add(X0,X1),X2,X3)
| sum(X0,add(X2,X1),X3) ),
inference(resolution,[status(thm)],[f109,f88]) ).
fof(f975,plain,
! [X0,X1,X2,X3] :
( ~ sum(add(X0,X1),X2,X3)
| sum(X0,add(X1,X2),X3) ),
inference(resolution,[status(thm)],[f109,f24]) ).
fof(f1099,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,multiply(X1,X0),X3)
| product(X2,X0,X3) ),
inference(resolution,[status(thm)],[f412,f23]) ).
fof(f1487,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f145,f23]) ).
fof(f1565,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[f1487,f80]) ).
fof(f1570,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(resolution,[status(thm)],[f1487,f52]) ).
fof(f1600,plain,
! [X0,X1] : product(multiply(multiply(X0,X1),X0),X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f79,f1487]) ).
fof(f1906,plain,
! [X0,X1] : product(X0,multiply(X1,multiply(X0,X1)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f1570,f23]) ).
fof(f1907,plain,
! [X0,X1] : product(multiply(X0,multiply(X1,X0)),X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1565,f1600]) ).
fof(f2513,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f549,f21]) ).
fof(f2527,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f2513,f96]) ).
fof(f2719,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,X1)
| sum(X0,multiply(X0,additive_inverse(X0)),X1) ),
inference(resolution,[status(thm)],[f431,f26]) ).
fof(f2720,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| sum(X0,multiply(X0,additive_identity),X1) ),
inference(resolution,[status(thm)],[f431,f22]) ).
fof(f2721,plain,
! [X0,X1,X2] :
( ~ product(X0,add(X1,X0),X2)
| sum(X0,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f431,f88]) ).
fof(f2722,plain,
! [X0,X1,X2] :
( ~ product(X0,add(X0,X1),X2)
| sum(X0,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f431,f24]) ).
fof(f2731,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),multiply(X0,X0)),
inference(resolution,[status(thm)],[f2720,f23]) ).
fof(f2732,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),X0),
inference(forward_demodulation,[status(thm)],[f79,f2731]) ).
fof(f2754,plain,
! [X0] : add(X0,multiply(X0,additive_identity)) = X0,
inference(resolution,[status(thm)],[f2732,f98]) ).
fof(f3073,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f553,f21]) ).
fof(f3106,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f3073,f98]) ).
fof(f3125,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f2527,f3106]) ).
fof(f3128,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X0) = additive_inverse(X1),
inference(paramodulation,[status(thm)],[f3106,f3106]) ).
fof(f3129,plain,
! [X0,X1] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f319,f3128]) ).
fof(f3138,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f319,f3106]) ).
fof(f3652,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f319,f3125]) ).
fof(f3700,plain,
! [X0] : add(additive_inverse(X0),X0) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f2754,f3138]) ).
fof(f3701,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f299,f3700]) ).
fof(f3712,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f3138,f3106]) ).
fof(f3713,plain,
! [X0,X1] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f319,f3712]) ).
fof(f3788,plain,
! [X0] : product(X0,multiply(additive_identity,multiply(X0,additive_identity)),additive_identity),
inference(paramodulation,[status(thm)],[f3701,f1906]) ).
fof(f3789,plain,
! [X0] : product(X0,multiply(additive_identity,additive_identity),additive_identity),
inference(forward_demodulation,[status(thm)],[f3701,f3788]) ).
fof(f3790,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f3701,f3789]) ).
fof(f3902,plain,
! [X0,X1] :
( ~ product(additive_identity,additive_inverse(X0),X1)
| sum(additive_inverse(X0),multiply(X0,additive_inverse(X0)),X1) ),
inference(resolution,[status(thm)],[f777,f25]) ).
fof(f3909,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| sum(X0,multiply(additive_identity,X0),X1) ),
inference(resolution,[status(thm)],[f777,f22]) ).
fof(f3910,plain,
! [X0,X1,X2] :
( ~ product(add(X0,X1),X1,X2)
| sum(X1,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f777,f88]) ).
fof(f3911,plain,
! [X0,X1,X2] :
( ~ product(add(X0,X1),X0,X2)
| sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f777,f24]) ).
fof(f4097,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
inference(resolution,[status(thm)],[f974,f88]) ).
fof(f4124,plain,
! [X0,X1,X2] :
( ~ sum(X0,multiply(X1,X0),X2)
| product(add(X1,X0),X0,X2) ),
inference(resolution,[status(thm)],[f1099,f88]) ).
fof(f4484,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
inference(resolution,[status(thm)],[f975,f24]) ).
fof(f4544,plain,
! [X0] : sum(X0,multiply(additive_identity,X0),multiply(X0,X0)),
inference(resolution,[status(thm)],[f3909,f23]) ).
fof(f4545,plain,
! [X0] : sum(X0,multiply(additive_identity,X0),X0),
inference(forward_demodulation,[status(thm)],[f79,f4544]) ).
fof(f4604,plain,
! [X0] : add(X0,multiply(additive_identity,X0)) = X0,
inference(resolution,[status(thm)],[f4545,f98]) ).
fof(f4642,plain,
! [X0] : add(additive_inverse(X0),X0) = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f4604,f3138]) ).
fof(f4643,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f299,f4642]) ).
fof(f4705,plain,
! [X0] : product(additive_identity,X0,multiply(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f4643,f1907]) ).
fof(f4706,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f4643,f4705]) ).
fof(f7483,plain,
! [X0] : sum(X0,multiply(X0,additive_inverse(X0)),additive_identity),
inference(resolution,[status(thm)],[f2719,f3790]) ).
fof(f7559,plain,
! [X0] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(resolution,[status(thm)],[f7483,f98]) ).
fof(f7639,plain,
! [X0] : add(multiply(X0,additive_inverse(X0)),additive_inverse(additive_identity)) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f7559,f3713]) ).
fof(f7640,plain,
! [X0] : add(additive_inverse(additive_identity),multiply(X0,additive_inverse(X0))) = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f319,f7639]) ).
fof(f7641,plain,
! [X0] : add(additive_identity,multiply(X0,additive_inverse(X0))) = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f99,f7640]) ).
fof(f7642,plain,
! [X0] : multiply(X0,additive_inverse(X0)) = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f101,f7641]) ).
fof(f7810,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
inference(resolution,[status(thm)],[f2721,f23]) ).
fof(f7836,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
inference(resolution,[status(thm)],[f2722,f23]) ).
fof(f9119,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
inference(resolution,[status(thm)],[f4097,f97]) ).
fof(f9913,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(resolution,[status(thm)],[f4484,f98]) ).
fof(f10619,plain,
! [X0,X1] :
( ~ product(additive_identity,additive_inverse(X0),X1)
| sum(additive_inverse(X0),additive_inverse(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f7642,f3902]) ).
fof(f10620,plain,
! [X0] : sum(additive_inverse(X0),additive_inverse(X0),additive_identity),
inference(resolution,[status(thm)],[f10619,f4706]) ).
fof(f10693,plain,
! [X0] : sum(X0,additive_inverse(additive_inverse(X0)),additive_identity),
inference(paramodulation,[status(thm)],[f2527,f10620]) ).
fof(f10694,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f2527,f10693]) ).
fof(f10806,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(resolution,[status(thm)],[f10694,f98]) ).
fof(f10869,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f10806,f3652]) ).
fof(f10870,plain,
! [X0] : X0 = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f100,f10869]) ).
fof(f11060,plain,
! [X0,X1] : add(X0,add(X1,X0)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f10870,f3713]) ).
fof(f11061,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f10870,f11060]) ).
fof(f11068,plain,
! [X0,X1] : add(X0,add(X0,X1)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f10870,f3129]) ).
fof(f11069,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f10870,f11068]) ).
fof(f12043,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,X0),X0)),
inference(resolution,[status(thm)],[f3910,f23]) ).
fof(f12064,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X0,X1),X0)),
inference(resolution,[status(thm)],[f3911,f23]) ).
fof(f12252,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f7810,f98]) ).
fof(f12383,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f7836,f98]) ).
fof(f12463,plain,
! [X0,X1] : product(add(X0,X1),X1,add(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[f4124,f88]) ).
fof(f12464,plain,
! [X0,X1] : product(add(X0,X1),X1,add(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f319,f12463]) ).
fof(f17071,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f9119,f9913]) ).
fof(f22472,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(resolution,[status(thm)],[f12043,f98]) ).
fof(f22636,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(resolution,[status(thm)],[f12064,f98]) ).
fof(f23657,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f12252,f12383]) ).
fof(f24605,plain,
! [X0,X1] : product(X0,add(X0,X1),add(add(X0,X1),multiply(X1,add(X0,X1)))),
inference(paramodulation,[status(thm)],[f11061,f12464]) ).
fof(f24606,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(multiply(X1,add(X0,X1)),X1))),
inference(forward_demodulation,[status(thm)],[f9119,f24605]) ).
fof(f24607,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(X1,multiply(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f17071,f24606]) ).
fof(f24608,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(add(X0,X1),X1)))),
inference(forward_demodulation,[status(thm)],[f12252,f24607]) ).
fof(f24609,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f23657,f24608]) ).
fof(f24610,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f11061,f24609]) ).
fof(f36589,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = multiply(add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f22472,f22636]) ).
fof(f38425,plain,
! [X0,X1] : product(X0,add(X0,X1),multiply(add(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f22472,f24610]) ).
fof(f38540,plain,
! [X0,X1] : product(X0,X1,multiply(add(add(X0,X1),X0),X0)),
inference(paramodulation,[status(thm)],[f11069,f38425]) ).
fof(f38541,plain,
! [X0,X1] : product(X0,X1,multiply(add(X0,add(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f36589,f38540]) ).
fof(f38542,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f11069,f38541]) ).
fof(f38735,plain,
product(b,a,c),
inference(paramodulation,[status(thm)],[f72,f38542]) ).
fof(f38736,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f38735,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : RNG008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.25 % Computer : n002.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon Apr 29 22:35:54 EDT 2024
% 0.07/0.25 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 34.32/4.66 % Refutation found
% 34.32/4.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 34.32/4.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 34.63/4.75 % Elapsed time: 4.473265 seconds
% 34.63/4.75 % CPU time: 35.190811 seconds
% 34.63/4.75 % Total memory used: 244.544 MB
% 34.63/4.75 % Net memory used: 228.017 MB
%------------------------------------------------------------------------------